lecture-notes
Math 210C. Centers of simply connected semisimple groups
Brian Conrad
Use in this reference: Linked author-hosted handout; factual center data are restated in original notation.
Relevant material: Center tables on pages 2–4; low-rank isomorphisms on page 4.
Dependent assertions
| Record | Assertion | Source locator |
|---|---|---|
| SU(2) | Center | Pages 1–2: type A₁ and SU(2) center μ₂ |
| SO(3) | Center | Page 4: SO(3) = SU(2)/μ₂; the adjoint A₁ group |
| SU(3) | Center | Page 3: type A₂ center μ₃, realized by scalar matrices in SU(3) |
| SU(3) | Topology and global form | Pages 2–4: centers of simply connected groups by root-system type |
| SU(3) | Explicit homomorphism | Pages 2–4: centers of simply connected groups by root-system type |
| PSU(3) | Definition | Pages 2–4: centers of simply connected groups by root-system type |
| PSU(3) | Fundamental group | Pages 2–4: centers of simply connected groups by root-system type |
| PSU(3) | Topology and global form | Pages 2–4: centers of simply connected groups by root-system type |
| PSU(3) | Related group | Pages 2–4: centers of simply connected groups by root-system type |
| PSU(3) | Explicit homomorphism | Pages 2–4: centers of simply connected groups by root-system type |
| Spin(4) | Real dimension | Page 4: D₂ = A₁ × A₁; dim Spin(4)=3+3=6 |
| Spin(4) | Center | Page 4: Spin(4) ≅ SU(2) × SU(2) with center μ₂ × μ₂ |
| Spin(4) | Rank | Page 4: D₂ = A₁ × A₁; rank 1+1=2 |
| Aᵣ | Center of compact simply connected group | Pages 2–4: centers of simply connected groups by root-system type |
| Aᵣ | Rank conventions and coincidences | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| Bᵣ | Center of compact simply connected group | Pages 2–4: centers of simply connected groups by root-system type |
| Bᵣ | Rank conventions and coincidences | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| Bᵣ | Rank conventions and coincidences | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| Cᵣ | Center of compact simply connected group | Pages 2–4: centers of simply connected groups by root-system type |
| Cᵣ | Rank conventions and coincidences | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| Cᵣ | Rank conventions and coincidences | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| Dᵣ | Center of compact simply connected group | Pages 2–4: centers of simply connected groups by root-system type |
| Dᵣ | Rank conventions and coincidences | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| Dᵣ | Rank conventions and coincidences | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| Dᵣ | Rank conventions and coincidences | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| Dᵣ | Rank conventions and coincidences | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| E₆ | Center of compact simply connected group | Pages 2–4: centers of simply connected groups by root-system type |
| E₇ | Center of compact simply connected group | Pages 2–4: centers of simply connected groups by root-system type |
| E₈ | Center of compact simply connected group | Pages 2–4: centers of simply connected groups by root-system type |
| F₄ | Center of compact simply connected group | Pages 2–4: centers of simply connected groups by root-system type |
| G₂ | Center of compact simply connected group | Pages 2–4: centers of simply connected groups by root-system type |
| sl(2, C) | Definition | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| sl(2, C) | Root-system type | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| sl(2, C) | Simple over C | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| sl(3, C) | Definition | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| sl(3, C) | Root-system type | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| sl(3, C) | Simple over C | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| sl(4, C) | Definition | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| sl(4, C) | Root-system type | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| sl(4, C) | Simple over C | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| sl(5, C) | Definition | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| sl(5, C) | Root-system type | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| sl(5, C) | Simple over C | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| so(5, C) ≅ sp(4, C) | Definition | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| so(5, C) ≅ sp(4, C) | Root-system type | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| so(5, C) ≅ sp(4, C) | Simple over C | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| so(5, C) ≅ sp(4, C) | C₂ low-rank coincidence | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| sp(6, C) | Definition | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| sp(6, C) | Root-system type | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| sp(6, C) | Simple over C | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| so(8, C) | Definition | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| so(8, C) | Root-system type | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| so(8, C) | Simple over C | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| so(10, C) | Definition | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| so(10, C) | Root-system type | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| so(10, C) | Simple over C | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| e₆(C) | Definition | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| e₆(C) | Root-system type | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| e₆(C) | Simple over C | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| e₇(C) | Definition | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| e₇(C) | Root-system type | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| e₇(C) | Simple over C | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| e₈(C) | Definition | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| e₈(C) | Root-system type | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| e₈(C) | Simple over C | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| f₄(C) | Definition | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| f₄(C) | Root-system type | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| f₄(C) | Simple over C | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| g₂(C) | Definition | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| g₂(C) | Root-system type | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| g₂(C) | Simple over C | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| sl(2, C) ⊕ sl(2, C) | Definition | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| sl(2, C) ⊕ sl(2, C) | Root-system type | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| sl(2, C) ⊕ sl(2, C) | Simple over C | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| sl(2, C) ⊕ sl(2, C) | Using the algebra record | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| C (zero bracket) | Definition | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| C (zero bracket) | Root-system type | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| C (zero bracket) | Simple over C | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| C (zero bracket) | Using the algebra record | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| sl(2, C) ⊕ C | Definition | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| sl(2, C) ⊕ C | Root-system type | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| sl(2, C) ⊕ C | Simple over C | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| sl(2, C) ⊕ C | Using the algebra record | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| su(2) | Definition | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| su(4) ≅ so(6) | Definition | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| sp(2) ≅ so(5) | Definition | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| sp(3) | Definition | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| su(2) ⊕ su(2) | Definition | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| u(1) | Definition | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| sl(2, R) | Definition | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| su(2,2) ≅ so(2,4) | Definition | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| sp(4, R) ≅ so(2,3) | Definition | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| sl(2, C) viewed over R | Definition | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| SU(4) | Center | Pages 2–4: centers of simply connected groups by root-system type |
| SU(4) | Global form | Pages 2–4: centers of simply connected groups by root-system type · Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| SU(4) | Global structure and topology | Pages 2–4: centers of simply connected groups by root-system type · Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| SU(4) | Explicit homomorphism | Pages 2–4: centers of simply connected groups by root-system type · Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| SU(4) | Explicit homomorphism | Pages 2–4: centers of simply connected groups by root-system type · Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| PSU(4) | Center | Pages 2–4: centers of simply connected groups by root-system type |
| PSU(4) | Global form | Pages 2–4: centers of simply connected groups by root-system type · Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| PSU(4) | Global structure and topology | Pages 2–4: centers of simply connected groups by root-system type · Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| PSU(4) | Explicit homomorphism | Pages 2–4: centers of simply connected groups by root-system type · Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| PSU(4) | Specified connected covering group | Pages 2–4: centers of simply connected groups by root-system type · Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| SU(5) | Center | Pages 2–4: centers of simply connected groups by root-system type |
| SU(5) | Global form | Pages 2–4: centers of simply connected groups by root-system type |
| SU(5) | Global structure and topology | Pages 2–4: centers of simply connected groups by root-system type |
| SO(4) | Center | Pages 2–4: centers of simply connected groups by root-system type |
| SO(4) | Global form | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| SO(4) | Global structure and topology | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| SO(4) | Explicit homomorphism | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| SO(4) | Specified connected covering group | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| SO(5) | Center | Pages 2–4: centers of simply connected groups by root-system type |
| SO(5) | Global form | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| SO(5) | Global structure and topology | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| SO(5) | Explicit homomorphism | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| SO(5) | Specified connected covering group | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| SO(6) | Center | Pages 2–4: centers of simply connected groups by root-system type |
| SO(6) | Global form | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms · Pages 2–4: centers of simply connected groups by root-system type |
| SO(6) | Global structure and topology | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms · Pages 2–4: centers of simply connected groups by root-system type |
| SO(6) | Explicit homomorphism | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms · Pages 2–4: centers of simply connected groups by root-system type |
| SO(6) | Specified connected covering group | Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms · Pages 2–4: centers of simply connected groups by root-system type |
| Sp(2) | Center | Pages 2–4: centers of simply connected groups by root-system type |
| Sp(2) | Global form | Pages 2–4: centers of simply connected groups by root-system type · Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| Sp(2) | Global structure and topology | Pages 2–4: centers of simply connected groups by root-system type · Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| Sp(2) | Explicit homomorphism | Pages 2–4: centers of simply connected groups by root-system type · Page 4: SO(3), SO(4), SO(5), and SO(6) low-rank isomorphisms |
| Sp(3) | Center | Pages 2–4: centers of simply connected groups by root-system type |
| Sp(3) | Global form | Pages 2–4: centers of simply connected groups by root-system type |
| Sp(3) | Global structure and topology | Pages 2–4: centers of simply connected groups by root-system type |
| Spin(8) | Center | Pages 2–4: centers of simply connected groups by root-system type |
| Spin(8) | Global form | Pages 2–4: centers of simply connected groups by root-system type |
| Spin(8) | Global structure and topology | Pages 2–4: centers of simply connected groups by root-system type |
| Spin(8) | Explicit homomorphism | Pages 2–4: centers of simply connected groups by root-system type |
| SO(8) | Center | Pages 2–4: centers of simply connected groups by root-system type |
| SO(8) | Global form | Pages 2–4: centers of simply connected groups by root-system type |
| SO(8) | Global structure and topology | Pages 2–4: centers of simply connected groups by root-system type |
| SO(8) | Explicit homomorphism | Pages 2–4: centers of simply connected groups by root-system type |
| SO(8) | Specified connected covering group | Pages 2–4: centers of simply connected groups by root-system type |
| PSO(8) | Center | Pages 2–4: centers of simply connected groups by root-system type |
| PSO(8) | Global form | Pages 2–4: centers of simply connected groups by root-system type |
| PSO(8) | Global structure and topology | Pages 2–4: centers of simply connected groups by root-system type |
| PSO(8) | Specified connected covering group | Pages 2–4: centers of simply connected groups by root-system type |
| Spin(10) | Center | Pages 2–4: centers of simply connected groups by root-system type |
| Spin(10) | Global form | Pages 2–4: centers of simply connected groups by root-system type |
| Spin(10) | Global structure and topology | Pages 2–4: centers of simply connected groups by root-system type |
| Spin(10) | Explicit homomorphism | Pages 2–4: centers of simply connected groups by root-system type |
| SO(10) | Center | Pages 2–4: centers of simply connected groups by root-system type |
| SO(10) | Global form | Pages 2–4: centers of simply connected groups by root-system type |
| SO(10) | Global structure and topology | Pages 2–4: centers of simply connected groups by root-system type |
| SO(10) | Explicit homomorphism | Pages 2–4: centers of simply connected groups by root-system type |
| SO(10) | Specified connected covering group | Pages 2–4: centers of simply connected groups by root-system type |
| G₂ compact | Center | Pages 2–4: centers of simply connected groups by root-system type |
| G₂ compact | Global form | Pages 2–4: centers of simply connected groups by root-system type |
| G₂ compact | Global structure and topology | Pages 2–4: centers of simply connected groups by root-system type |
| F₄ compact | Center | Pages 2–4: centers of simply connected groups by root-system type |
| F₄ compact | Global form | Pages 2–4: centers of simply connected groups by root-system type |
| F₄ compact | Global structure and topology | Pages 2–4: centers of simply connected groups by root-system type |
| E₆ compact, simply connected | Center | Pages 2–4: centers of simply connected groups by root-system type |
| E₆ compact, simply connected | Global form | Pages 2–4: centers of simply connected groups by root-system type |
| E₆ compact, simply connected | Global structure and topology | Pages 2–4: centers of simply connected groups by root-system type |
| E₇ compact, simply connected | Center | Pages 2–4: centers of simply connected groups by root-system type |
| E₇ compact, simply connected | Global form | Pages 2–4: centers of simply connected groups by root-system type |
| E₇ compact, simply connected | Global structure and topology | Pages 2–4: centers of simply connected groups by root-system type |
| E₈ compact | Center | Pages 2–4: centers of simply connected groups by root-system type |
| E₈ compact | Global form | Pages 2–4: centers of simply connected groups by root-system type |
| E₈ compact | Global structure and topology | Pages 2–4: centers of simply connected groups by root-system type |
| E₈ compact | Representation category and descent | Pages 2–4: centers of simply connected groups by root-system type |
| E₆ compact, adjoint | Center | Pages 2–4: centers of simply connected groups by root-system type |
| E₆ compact, adjoint | Global form | Pages 2–4: centers of simply connected groups by root-system type |
| E₆ compact, adjoint | Global structure and topology | Pages 2–4: centers of simply connected groups by root-system type |
| E₆ compact, adjoint | Specified connected covering group | Pages 2–4: centers of simply connected groups by root-system type |
| E₇ compact, adjoint | Center | Pages 2–4: centers of simply connected groups by root-system type |
| E₇ compact, adjoint | Global form | Pages 2–4: centers of simply connected groups by root-system type |
| E₇ compact, adjoint | Global structure and topology | Pages 2–4: centers of simply connected groups by root-system type |
| E₇ compact, adjoint | Specified connected covering group | Pages 2–4: centers of simply connected groups by root-system type |
| SU(3) → PSU(3) | Definition | Pages 2–4: centers of simply connected groups by root-system type |
| SU(3) → PSU(3) | Domain | Pages 2–4: centers of simply connected groups by root-system type |
| SU(3) → PSU(3) | Codomain | Pages 2–4: centers of simply connected groups by root-system type |
| SU(3) → PSU(3) | Specified homomorphism | Pages 2–4: centers of simply connected groups by root-system type |
| SU(3) → PSU(3) | Kernel | Pages 2–4: centers of simply connected groups by root-system type |
| SU(3) → PSU(3) | Image | Pages 2–4: centers of simply connected groups by root-system type |
| SU(3) → PSU(3) | Injective | Pages 2–4: centers of simply connected groups by root-system type |
| SU(3) → PSU(3) | Surjective | Pages 2–4: centers of simply connected groups by root-system type |
| SU(3) → PSU(3) | Covering degree | Pages 2–4: centers of simply connected groups by root-system type |
| SU(3) → PSU(3) | Global and representation consequences | Pages 2–4: centers of simply connected groups by root-system type |
| SU(3) → PSU(3) | Domain group | Pages 2–4: centers of simply connected groups by root-system type |
| SU(3) → PSU(3) | Codomain group | Pages 2–4: centers of simply connected groups by root-system type |
| SU(4) → PSU(4) | Definition | Pages 2–4: centers of simply connected groups by root-system type |
| SU(4) → PSU(4) | Domain | Pages 2–4: centers of simply connected groups by root-system type |
| SU(4) → PSU(4) | Codomain | Pages 2–4: centers of simply connected groups by root-system type |
| SU(4) → PSU(4) | Specified homomorphism | Pages 2–4: centers of simply connected groups by root-system type |
| SU(4) → PSU(4) | Kernel | Pages 2–4: centers of simply connected groups by root-system type |
| SU(4) → PSU(4) | Image | Pages 2–4: centers of simply connected groups by root-system type |
| SU(4) → PSU(4) | Injective | Pages 2–4: centers of simply connected groups by root-system type |
| SU(4) → PSU(4) | Surjective | Pages 2–4: centers of simply connected groups by root-system type |
| SU(4) → PSU(4) | Covering degree | Pages 2–4: centers of simply connected groups by root-system type |
| SU(4) → PSU(4) | Global and representation consequences | Pages 2–4: centers of simply connected groups by root-system type |
| SU(4) → PSU(4) | Domain group | Pages 2–4: centers of simply connected groups by root-system type |
| SU(4) → PSU(4) | Codomain group | Pages 2–4: centers of simply connected groups by root-system type |
| A1 · (1) | Definition | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A1 · (1) | Complex dimension | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A1 · (1) | Coefficient field | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A1 · (1) | Quadratic Casimir C₂ | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A1 · (1) | Quadratic index T(R) | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A1 · (1) | Reality type | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A1 · (1) | Conjugate highest weight | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A1 · (1) | Descends to the adjoint global form | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A1 · (1) | Order of central kernel | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A1 · (1) | Highest weight and conventions | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A1 · (1) | Global form and center | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A1 · (1) | Use in a calculation | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A1 · (1) | Representation domain | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A1 · (2) | Definition | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A1 · (2) | Complex dimension | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A1 · (2) | Coefficient field | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A1 · (2) | Quadratic Casimir C₂ | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A1 · (2) | Quadratic index T(R) | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A1 · (2) | Reality type | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A1 · (2) | Conjugate highest weight | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A1 · (2) | Descends to the adjoint global form | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A1 · (2) | Order of central kernel | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A1 · (2) | Highest weight and conventions | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A1 · (2) | Global form and center | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A1 · (2) | Use in a calculation | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A1 · (2) | Representation domain | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (1,0) | Definition | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (1,0) | Complex dimension | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (1,0) | Coefficient field | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (1,0) | Quadratic Casimir C₂ | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (1,0) | Quadratic index T(R) | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (1,0) | Reality type | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (1,0) | Conjugate highest weight | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (1,0) | Descends to the adjoint global form | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (1,0) | Order of central kernel | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (1,0) | Highest weight and conventions | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (1,0) | Global form and center | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (1,0) | Use in a calculation | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (1,0) | Representation domain | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (0,1) | Definition | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (0,1) | Complex dimension | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (0,1) | Coefficient field | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (0,1) | Quadratic Casimir C₂ | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (0,1) | Quadratic index T(R) | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (0,1) | Reality type | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (0,1) | Conjugate highest weight | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (0,1) | Descends to the adjoint global form | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (0,1) | Order of central kernel | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (0,1) | Highest weight and conventions | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (0,1) | Global form and center | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (0,1) | Use in a calculation | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (0,1) | Representation domain | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (1,1) | Definition | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (1,1) | Complex dimension | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (1,1) | Coefficient field | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (1,1) | Quadratic Casimir C₂ | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (1,1) | Quadratic index T(R) | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (1,1) | Reality type | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (1,1) | Conjugate highest weight | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (1,1) | Descends to the adjoint global form | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (1,1) | Order of central kernel | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (1,1) | Highest weight and conventions | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (1,1) | Global form and center | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (1,1) | Use in a calculation | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (1,1) | Representation domain | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (2,0) | Definition | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (2,0) | Complex dimension | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (2,0) | Coefficient field | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (2,0) | Quadratic Casimir C₂ | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (2,0) | Quadratic index T(R) | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (2,0) | Reality type | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (2,0) | Conjugate highest weight | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (2,0) | Descends to the adjoint global form | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (2,0) | Order of central kernel | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (2,0) | Highest weight and conventions | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (2,0) | Global form and center | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (2,0) | Use in a calculation | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (2,0) | Representation domain | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (3,0) | Definition | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (3,0) | Complex dimension | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (3,0) | Coefficient field | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (3,0) | Quadratic Casimir C₂ | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (3,0) | Quadratic index T(R) | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (3,0) | Reality type | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (3,0) | Conjugate highest weight | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (3,0) | Descends to the adjoint global form | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (3,0) | Order of central kernel | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (3,0) | Highest weight and conventions | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (3,0) | Global form and center | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (3,0) | Use in a calculation | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (3,0) | Representation domain | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (2,2) | Definition | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (2,2) | Complex dimension | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (2,2) | Coefficient field | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (2,2) | Quadratic Casimir C₂ | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (2,2) | Quadratic index T(R) | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (2,2) | Reality type | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (2,2) | Conjugate highest weight | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (2,2) | Descends to the adjoint global form | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (2,2) | Order of central kernel | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (2,2) | Highest weight and conventions | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (2,2) | Global form and center | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (2,2) | Use in a calculation | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A2 · (2,2) | Representation domain | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A3 · (1,0,0) | Definition | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A3 · (1,0,0) | Complex dimension | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A3 · (1,0,0) | Coefficient field | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A3 · (1,0,0) | Quadratic Casimir C₂ | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A3 · (1,0,0) | Quadratic index T(R) | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A3 · (1,0,0) | Reality type | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A3 · (1,0,0) | Conjugate highest weight | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A3 · (1,0,0) | Descends to the adjoint global form | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A3 · (1,0,0) | Order of central kernel | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A3 · (1,0,0) | Highest weight and conventions | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A3 · (1,0,0) | Global form and center | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A3 · (1,0,0) | Use in a calculation | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A3 · (1,0,0) | Representation domain | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A3 · (0,1,0) | Definition | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A3 · (0,1,0) | Complex dimension | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A3 · (0,1,0) | Coefficient field | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A3 · (0,1,0) | Quadratic Casimir C₂ | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A3 · (0,1,0) | Quadratic index T(R) | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A3 · (0,1,0) | Reality type | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A3 · (0,1,0) | Conjugate highest weight | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A3 · (0,1,0) | Descends to the adjoint global form | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A3 · (0,1,0) | Order of central kernel | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A3 · (0,1,0) | Highest weight and conventions | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A3 · (0,1,0) | Global form and center | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A3 · (0,1,0) | Use in a calculation | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A3 · (0,1,0) | Representation domain | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A3 · (1,0,1) | Definition | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A3 · (1,0,1) | Complex dimension | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A3 · (1,0,1) | Coefficient field | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A3 · (1,0,1) | Quadratic Casimir C₂ | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A3 · (1,0,1) | Quadratic index T(R) | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A3 · (1,0,1) | Reality type | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A3 · (1,0,1) | Conjugate highest weight | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A3 · (1,0,1) | Descends to the adjoint global form | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A3 · (1,0,1) | Order of central kernel | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A3 · (1,0,1) | Highest weight and conventions | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A3 · (1,0,1) | Global form and center | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A3 · (1,0,1) | Use in a calculation | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A3 · (1,0,1) | Representation domain | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A4 · (1,0,0,0) | Definition | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A4 · (1,0,0,0) | Complex dimension | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A4 · (1,0,0,0) | Coefficient field | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A4 · (1,0,0,0) | Quadratic Casimir C₂ | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A4 · (1,0,0,0) | Quadratic index T(R) | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A4 · (1,0,0,0) | Reality type | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A4 · (1,0,0,0) | Conjugate highest weight | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A4 · (1,0,0,0) | Descends to the adjoint global form | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A4 · (1,0,0,0) | Order of central kernel | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A4 · (1,0,0,0) | Highest weight and conventions | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A4 · (1,0,0,0) | Global form and center | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A4 · (1,0,0,0) | Use in a calculation | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A4 · (1,0,0,0) | Representation domain | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A4 · (0,1,0,0) | Definition | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A4 · (0,1,0,0) | Complex dimension | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A4 · (0,1,0,0) | Coefficient field | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A4 · (0,1,0,0) | Quadratic Casimir C₂ | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A4 · (0,1,0,0) | Quadratic index T(R) | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A4 · (0,1,0,0) | Reality type | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A4 · (0,1,0,0) | Conjugate highest weight | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A4 · (0,1,0,0) | Descends to the adjoint global form | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A4 · (0,1,0,0) | Order of central kernel | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A4 · (0,1,0,0) | Highest weight and conventions | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A4 · (0,1,0,0) | Global form and center | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A4 · (0,1,0,0) | Use in a calculation | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A4 · (0,1,0,0) | Representation domain | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A4 · (1,0,0,1) | Definition | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A4 · (1,0,0,1) | Complex dimension | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A4 · (1,0,0,1) | Coefficient field | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A4 · (1,0,0,1) | Quadratic Casimir C₂ | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A4 · (1,0,0,1) | Quadratic index T(R) | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A4 · (1,0,0,1) | Reality type | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A4 · (1,0,0,1) | Conjugate highest weight | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A4 · (1,0,0,1) | Descends to the adjoint global form | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A4 · (1,0,0,1) | Order of central kernel | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A4 · (1,0,0,1) | Highest weight and conventions | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A4 · (1,0,0,1) | Global form and center | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A4 · (1,0,0,1) | Use in a calculation | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| A4 · (1,0,0,1) | Representation domain | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| C2 · (1,0) | Definition | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| C2 · (1,0) | Complex dimension | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| C2 · (1,0) | Coefficient field | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| C2 · (1,0) | Quadratic Casimir C₂ | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| C2 · (1,0) | Quadratic index T(R) | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| C2 · (1,0) | Reality type | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| C2 · (1,0) | Conjugate highest weight | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| C2 · (1,0) | Descends to the adjoint global form | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| C2 · (1,0) | Order of central kernel | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| C2 · (1,0) | Highest weight and conventions | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| C2 · (1,0) | Global form and center | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| C2 · (1,0) | Use in a calculation | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| C2 · (1,0) | Representation domain | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| C2 · (0,1) | Definition | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| C2 · (0,1) | Complex dimension | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| C2 · (0,1) | Coefficient field | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| C2 · (0,1) | Quadratic Casimir C₂ | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| C2 · (0,1) | Quadratic index T(R) | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| C2 · (0,1) | Reality type | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| C2 · (0,1) | Conjugate highest weight | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| C2 · (0,1) | Descends to the adjoint global form | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| C2 · (0,1) | Order of central kernel | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| C2 · (0,1) | Highest weight and conventions | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| C2 · (0,1) | Global form and center | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| C2 · (0,1) | Use in a calculation | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| C2 · (0,1) | Representation domain | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D4 · (1,0,0,0) | Definition | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D4 · (1,0,0,0) | Complex dimension | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D4 · (1,0,0,0) | Coefficient field | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D4 · (1,0,0,0) | Quadratic Casimir C₂ | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D4 · (1,0,0,0) | Quadratic index T(R) | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D4 · (1,0,0,0) | Reality type | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D4 · (1,0,0,0) | Conjugate highest weight | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D4 · (1,0,0,0) | Descends to the adjoint global form | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D4 · (1,0,0,0) | Order of central kernel | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D4 · (1,0,0,0) | Highest weight and conventions | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D4 · (1,0,0,0) | Global form and center | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D4 · (1,0,0,0) | Use in a calculation | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D4 · (1,0,0,0) | Representation domain | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D4 · (0,0,1,0) | Definition | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D4 · (0,0,1,0) | Complex dimension | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D4 · (0,0,1,0) | Coefficient field | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D4 · (0,0,1,0) | Quadratic Casimir C₂ | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D4 · (0,0,1,0) | Quadratic index T(R) | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D4 · (0,0,1,0) | Reality type | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D4 · (0,0,1,0) | Conjugate highest weight | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D4 · (0,0,1,0) | Descends to the adjoint global form | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D4 · (0,0,1,0) | Order of central kernel | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D4 · (0,0,1,0) | Highest weight and conventions | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D4 · (0,0,1,0) | Global form and center | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D4 · (0,0,1,0) | Use in a calculation | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D4 · (0,0,1,0) | Representation domain | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D4 · (0,0,0,1) | Definition | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D4 · (0,0,0,1) | Complex dimension | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D4 · (0,0,0,1) | Coefficient field | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D4 · (0,0,0,1) | Quadratic Casimir C₂ | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D4 · (0,0,0,1) | Quadratic index T(R) | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D4 · (0,0,0,1) | Reality type | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D4 · (0,0,0,1) | Conjugate highest weight | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D4 · (0,0,0,1) | Descends to the adjoint global form | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D4 · (0,0,0,1) | Order of central kernel | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D4 · (0,0,0,1) | Highest weight and conventions | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D4 · (0,0,0,1) | Global form and center | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D4 · (0,0,0,1) | Use in a calculation | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D4 · (0,0,0,1) | Representation domain | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (1,0,0,0,0) | Definition | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (1,0,0,0,0) | Complex dimension | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (1,0,0,0,0) | Coefficient field | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (1,0,0,0,0) | Quadratic Casimir C₂ | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (1,0,0,0,0) | Quadratic index T(R) | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (1,0,0,0,0) | Reality type | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (1,0,0,0,0) | Conjugate highest weight | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (1,0,0,0,0) | Descends to the adjoint global form | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (1,0,0,0,0) | Order of central kernel | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (1,0,0,0,0) | Highest weight and conventions | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (1,0,0,0,0) | Global form and center | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (1,0,0,0,0) | Use in a calculation | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (1,0,0,0,0) | Representation domain | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (0,0,0,0,1) | Definition | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (0,0,0,0,1) | Complex dimension | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (0,0,0,0,1) | Coefficient field | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (0,0,0,0,1) | Quadratic Casimir C₂ | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (0,0,0,0,1) | Quadratic index T(R) | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (0,0,0,0,1) | Reality type | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (0,0,0,0,1) | Conjugate highest weight | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (0,0,0,0,1) | Descends to the adjoint global form | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (0,0,0,0,1) | Order of central kernel | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (0,0,0,0,1) | Highest weight and conventions | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (0,0,0,0,1) | Global form and center | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (0,0,0,0,1) | Use in a calculation | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (0,0,0,0,1) | Representation domain | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (0,0,0,1,0) | Definition | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (0,0,0,1,0) | Complex dimension | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (0,0,0,1,0) | Coefficient field | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (0,0,0,1,0) | Quadratic Casimir C₂ | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (0,0,0,1,0) | Quadratic index T(R) | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (0,0,0,1,0) | Reality type | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (0,0,0,1,0) | Conjugate highest weight | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (0,0,0,1,0) | Descends to the adjoint global form | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (0,0,0,1,0) | Order of central kernel | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (0,0,0,1,0) | Highest weight and conventions | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (0,0,0,1,0) | Global form and center | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (0,0,0,1,0) | Use in a calculation | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (0,0,0,1,0) | Representation domain | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (0,1,0,0,0) | Definition | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (0,1,0,0,0) | Complex dimension | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (0,1,0,0,0) | Coefficient field | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (0,1,0,0,0) | Quadratic Casimir C₂ | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (0,1,0,0,0) | Quadratic index T(R) | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (0,1,0,0,0) | Reality type | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (0,1,0,0,0) | Conjugate highest weight | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (0,1,0,0,0) | Descends to the adjoint global form | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (0,1,0,0,0) | Order of central kernel | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (0,1,0,0,0) | Highest weight and conventions | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (0,1,0,0,0) | Global form and center | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (0,1,0,0,0) | Use in a calculation | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| D5 · (0,1,0,0,0) | Representation domain | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| G2 · (1,0) | Definition | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| G2 · (1,0) | Complex dimension | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| G2 · (1,0) | Coefficient field | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| G2 · (1,0) | Quadratic Casimir C₂ | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| G2 · (1,0) | Quadratic index T(R) | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| G2 · (1,0) | Reality type | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| G2 · (1,0) | Conjugate highest weight | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| G2 · (1,0) | Descends to the adjoint global form | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| G2 · (1,0) | Order of central kernel | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| G2 · (1,0) | Highest weight and conventions | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| G2 · (1,0) | Global form and center | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| G2 · (1,0) | Use in a calculation | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| G2 · (1,0) | Representation domain | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| G2 · (0,1) | Definition | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| G2 · (0,1) | Complex dimension | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| G2 · (0,1) | Coefficient field | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| G2 · (0,1) | Quadratic Casimir C₂ | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| G2 · (0,1) | Quadratic index T(R) | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| G2 · (0,1) | Reality type | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| G2 · (0,1) | Conjugate highest weight | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| G2 · (0,1) | Descends to the adjoint global form | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| G2 · (0,1) | Order of central kernel | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| G2 · (0,1) | Highest weight and conventions | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| G2 · (0,1) | Global form and center | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| G2 · (0,1) | Use in a calculation | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| G2 · (0,1) | Representation domain | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| F4 · (0,0,0,1) | Definition | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| F4 · (0,0,0,1) | Complex dimension | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| F4 · (0,0,0,1) | Coefficient field | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| F4 · (0,0,0,1) | Quadratic Casimir C₂ | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| F4 · (0,0,0,1) | Quadratic index T(R) | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| F4 · (0,0,0,1) | Reality type | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| F4 · (0,0,0,1) | Conjugate highest weight | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| F4 · (0,0,0,1) | Descends to the adjoint global form | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| F4 · (0,0,0,1) | Order of central kernel | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| F4 · (0,0,0,1) | Highest weight and conventions | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| F4 · (0,0,0,1) | Global form and center | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| F4 · (0,0,0,1) | Use in a calculation | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| F4 · (0,0,0,1) | Representation domain | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| F4 · (1,0,0,0) | Definition | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| F4 · (1,0,0,0) | Complex dimension | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| F4 · (1,0,0,0) | Coefficient field | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| F4 · (1,0,0,0) | Quadratic Casimir C₂ | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| F4 · (1,0,0,0) | Quadratic index T(R) | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| F4 · (1,0,0,0) | Reality type | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| F4 · (1,0,0,0) | Conjugate highest weight | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| F4 · (1,0,0,0) | Descends to the adjoint global form | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| F4 · (1,0,0,0) | Order of central kernel | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| F4 · (1,0,0,0) | Highest weight and conventions | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| F4 · (1,0,0,0) | Global form and center | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| F4 · (1,0,0,0) | Use in a calculation | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| F4 · (1,0,0,0) | Representation domain | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E6 · (1,0,0,0,0,0) | Definition | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E6 · (1,0,0,0,0,0) | Complex dimension | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E6 · (1,0,0,0,0,0) | Coefficient field | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E6 · (1,0,0,0,0,0) | Quadratic Casimir C₂ | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E6 · (1,0,0,0,0,0) | Quadratic index T(R) | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E6 · (1,0,0,0,0,0) | Reality type | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E6 · (1,0,0,0,0,0) | Conjugate highest weight | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E6 · (1,0,0,0,0,0) | Descends to the adjoint global form | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E6 · (1,0,0,0,0,0) | Order of central kernel | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E6 · (1,0,0,0,0,0) | Highest weight and conventions | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E6 · (1,0,0,0,0,0) | Global form and center | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E6 · (1,0,0,0,0,0) | Use in a calculation | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E6 · (1,0,0,0,0,0) | Representation domain | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E6 · (0,1,0,0,0,0) | Definition | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E6 · (0,1,0,0,0,0) | Complex dimension | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E6 · (0,1,0,0,0,0) | Coefficient field | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E6 · (0,1,0,0,0,0) | Quadratic Casimir C₂ | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E6 · (0,1,0,0,0,0) | Quadratic index T(R) | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E6 · (0,1,0,0,0,0) | Reality type | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E6 · (0,1,0,0,0,0) | Conjugate highest weight | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E6 · (0,1,0,0,0,0) | Descends to the adjoint global form | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E6 · (0,1,0,0,0,0) | Order of central kernel | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E6 · (0,1,0,0,0,0) | Highest weight and conventions | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E6 · (0,1,0,0,0,0) | Global form and center | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E6 · (0,1,0,0,0,0) | Use in a calculation | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E6 · (0,1,0,0,0,0) | Representation domain | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E7 · (0,0,0,0,0,0,1) | Definition | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E7 · (0,0,0,0,0,0,1) | Complex dimension | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E7 · (0,0,0,0,0,0,1) | Coefficient field | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E7 · (0,0,0,0,0,0,1) | Quadratic Casimir C₂ | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E7 · (0,0,0,0,0,0,1) | Quadratic index T(R) | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E7 · (0,0,0,0,0,0,1) | Reality type | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E7 · (0,0,0,0,0,0,1) | Conjugate highest weight | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E7 · (0,0,0,0,0,0,1) | Descends to the adjoint global form | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E7 · (0,0,0,0,0,0,1) | Order of central kernel | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E7 · (0,0,0,0,0,0,1) | Highest weight and conventions | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E7 · (0,0,0,0,0,0,1) | Global form and center | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E7 · (0,0,0,0,0,0,1) | Use in a calculation | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E7 · (0,0,0,0,0,0,1) | Representation domain | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E7 · (1,0,0,0,0,0,0) | Definition | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E7 · (1,0,0,0,0,0,0) | Complex dimension | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E7 · (1,0,0,0,0,0,0) | Coefficient field | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E7 · (1,0,0,0,0,0,0) | Quadratic Casimir C₂ | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E7 · (1,0,0,0,0,0,0) | Quadratic index T(R) | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E7 · (1,0,0,0,0,0,0) | Reality type | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E7 · (1,0,0,0,0,0,0) | Conjugate highest weight | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E7 · (1,0,0,0,0,0,0) | Descends to the adjoint global form | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E7 · (1,0,0,0,0,0,0) | Order of central kernel | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E7 · (1,0,0,0,0,0,0) | Highest weight and conventions | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E7 · (1,0,0,0,0,0,0) | Global form and center | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E7 · (1,0,0,0,0,0,0) | Use in a calculation | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E7 · (1,0,0,0,0,0,0) | Representation domain | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E8 · (0,0,0,0,0,0,0,1) | Definition | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E8 · (0,0,0,0,0,0,0,1) | Complex dimension | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E8 · (0,0,0,0,0,0,0,1) | Coefficient field | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E8 · (0,0,0,0,0,0,0,1) | Quadratic Casimir C₂ | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E8 · (0,0,0,0,0,0,0,1) | Quadratic index T(R) | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E8 · (0,0,0,0,0,0,0,1) | Reality type | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E8 · (0,0,0,0,0,0,0,1) | Conjugate highest weight | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E8 · (0,0,0,0,0,0,0,1) | Descends to the adjoint global form | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E8 · (0,0,0,0,0,0,0,1) | Order of central kernel | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E8 · (0,0,0,0,0,0,0,1) | Highest weight and conventions | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E8 · (0,0,0,0,0,0,0,1) | Global form and center | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E8 · (0,0,0,0,0,0,0,1) | Use in a calculation | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |
| E8 · (0,0,0,0,0,0,0,1) | Representation domain | Pages 1–4: the center is dual to P/Q, with classical and exceptional types tabulated. |