lecture-notes
Lie Groups and Lie Algebras I
Pavel Etingof
Use in this reference: Linked primary source. Original algorithms and explanatory prose; no upstream software or document text is redistributed.
Relevant material: Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations.
Dependent assertions
| Record | Assertion | Source locator |
|---|---|---|
| A1 · (1) | Definition | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A1 · (1) | Complex dimension | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A1 · (1) | Coefficient field | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A1 · (1) | Quadratic Casimir C₂ | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A1 · (1) | Quadratic index T(R) | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A1 · (1) | Reality type | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A1 · (1) | Conjugate highest weight | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A1 · (1) | Descends to the adjoint global form | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A1 · (1) | Order of central kernel | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A1 · (1) | Highest weight and conventions | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A1 · (1) | Global form and center | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A1 · (1) | Use in a calculation | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A1 · (1) | Representation domain | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A1 · (2) | Definition | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A1 · (2) | Complex dimension | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A1 · (2) | Coefficient field | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A1 · (2) | Quadratic Casimir C₂ | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A1 · (2) | Quadratic index T(R) | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A1 · (2) | Reality type | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A1 · (2) | Conjugate highest weight | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A1 · (2) | Descends to the adjoint global form | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A1 · (2) | Order of central kernel | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A1 · (2) | Highest weight and conventions | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A1 · (2) | Global form and center | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A1 · (2) | Use in a calculation | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A1 · (2) | Representation domain | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (1,0) | Definition | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (1,0) | Complex dimension | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (1,0) | Coefficient field | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (1,0) | Quadratic Casimir C₂ | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (1,0) | Quadratic index T(R) | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (1,0) | Reality type | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (1,0) | Conjugate highest weight | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (1,0) | Descends to the adjoint global form | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (1,0) | Order of central kernel | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (1,0) | Highest weight and conventions | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (1,0) | Global form and center | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (1,0) | Use in a calculation | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (1,0) | Representation domain | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (0,1) | Definition | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (0,1) | Complex dimension | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (0,1) | Coefficient field | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (0,1) | Quadratic Casimir C₂ | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (0,1) | Quadratic index T(R) | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (0,1) | Reality type | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (0,1) | Conjugate highest weight | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (0,1) | Descends to the adjoint global form | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (0,1) | Order of central kernel | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (0,1) | Highest weight and conventions | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (0,1) | Global form and center | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (0,1) | Use in a calculation | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (0,1) | Representation domain | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (1,1) | Definition | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (1,1) | Complex dimension | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (1,1) | Coefficient field | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (1,1) | Quadratic Casimir C₂ | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (1,1) | Quadratic index T(R) | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (1,1) | Reality type | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (1,1) | Conjugate highest weight | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (1,1) | Descends to the adjoint global form | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (1,1) | Order of central kernel | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (1,1) | Highest weight and conventions | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (1,1) | Global form and center | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (1,1) | Use in a calculation | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (1,1) | Representation domain | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (2,0) | Definition | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (2,0) | Complex dimension | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (2,0) | Coefficient field | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (2,0) | Quadratic Casimir C₂ | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (2,0) | Quadratic index T(R) | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (2,0) | Reality type | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (2,0) | Conjugate highest weight | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (2,0) | Descends to the adjoint global form | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (2,0) | Order of central kernel | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (2,0) | Highest weight and conventions | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (2,0) | Global form and center | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (2,0) | Use in a calculation | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (2,0) | Representation domain | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (3,0) | Definition | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (3,0) | Complex dimension | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (3,0) | Coefficient field | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (3,0) | Quadratic Casimir C₂ | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (3,0) | Quadratic index T(R) | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (3,0) | Reality type | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (3,0) | Conjugate highest weight | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (3,0) | Descends to the adjoint global form | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (3,0) | Order of central kernel | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (3,0) | Highest weight and conventions | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (3,0) | Global form and center | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (3,0) | Use in a calculation | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (3,0) | Representation domain | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (2,2) | Definition | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (2,2) | Complex dimension | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (2,2) | Coefficient field | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (2,2) | Quadratic Casimir C₂ | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (2,2) | Quadratic index T(R) | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (2,2) | Reality type | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (2,2) | Conjugate highest weight | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (2,2) | Descends to the adjoint global form | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (2,2) | Order of central kernel | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (2,2) | Highest weight and conventions | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (2,2) | Global form and center | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (2,2) | Use in a calculation | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A2 · (2,2) | Representation domain | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A3 · (1,0,0) | Definition | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A3 · (1,0,0) | Complex dimension | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A3 · (1,0,0) | Coefficient field | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A3 · (1,0,0) | Quadratic Casimir C₂ | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A3 · (1,0,0) | Quadratic index T(R) | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A3 · (1,0,0) | Reality type | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A3 · (1,0,0) | Conjugate highest weight | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A3 · (1,0,0) | Descends to the adjoint global form | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A3 · (1,0,0) | Order of central kernel | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A3 · (1,0,0) | Highest weight and conventions | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A3 · (1,0,0) | Global form and center | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A3 · (1,0,0) | Use in a calculation | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A3 · (1,0,0) | Representation domain | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A3 · (0,1,0) | Definition | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A3 · (0,1,0) | Complex dimension | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A3 · (0,1,0) | Coefficient field | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A3 · (0,1,0) | Quadratic Casimir C₂ | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A3 · (0,1,0) | Quadratic index T(R) | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A3 · (0,1,0) | Reality type | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A3 · (0,1,0) | Conjugate highest weight | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A3 · (0,1,0) | Descends to the adjoint global form | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A3 · (0,1,0) | Order of central kernel | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A3 · (0,1,0) | Highest weight and conventions | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A3 · (0,1,0) | Global form and center | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A3 · (0,1,0) | Use in a calculation | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A3 · (0,1,0) | Representation domain | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A3 · (1,0,1) | Definition | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A3 · (1,0,1) | Complex dimension | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A3 · (1,0,1) | Coefficient field | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A3 · (1,0,1) | Quadratic Casimir C₂ | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A3 · (1,0,1) | Quadratic index T(R) | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A3 · (1,0,1) | Reality type | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A3 · (1,0,1) | Conjugate highest weight | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A3 · (1,0,1) | Descends to the adjoint global form | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A3 · (1,0,1) | Order of central kernel | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A3 · (1,0,1) | Highest weight and conventions | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A3 · (1,0,1) | Global form and center | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A3 · (1,0,1) | Use in a calculation | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A3 · (1,0,1) | Representation domain | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A4 · (1,0,0,0) | Definition | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A4 · (1,0,0,0) | Complex dimension | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A4 · (1,0,0,0) | Coefficient field | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A4 · (1,0,0,0) | Quadratic Casimir C₂ | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A4 · (1,0,0,0) | Quadratic index T(R) | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A4 · (1,0,0,0) | Reality type | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A4 · (1,0,0,0) | Conjugate highest weight | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A4 · (1,0,0,0) | Descends to the adjoint global form | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A4 · (1,0,0,0) | Order of central kernel | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A4 · (1,0,0,0) | Highest weight and conventions | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A4 · (1,0,0,0) | Global form and center | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A4 · (1,0,0,0) | Use in a calculation | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A4 · (1,0,0,0) | Representation domain | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A4 · (0,1,0,0) | Definition | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A4 · (0,1,0,0) | Complex dimension | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A4 · (0,1,0,0) | Coefficient field | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A4 · (0,1,0,0) | Quadratic Casimir C₂ | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A4 · (0,1,0,0) | Quadratic index T(R) | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A4 · (0,1,0,0) | Reality type | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A4 · (0,1,0,0) | Conjugate highest weight | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A4 · (0,1,0,0) | Descends to the adjoint global form | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A4 · (0,1,0,0) | Order of central kernel | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A4 · (0,1,0,0) | Highest weight and conventions | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A4 · (0,1,0,0) | Global form and center | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A4 · (0,1,0,0) | Use in a calculation | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A4 · (0,1,0,0) | Representation domain | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A4 · (1,0,0,1) | Definition | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A4 · (1,0,0,1) | Complex dimension | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A4 · (1,0,0,1) | Coefficient field | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A4 · (1,0,0,1) | Quadratic Casimir C₂ | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A4 · (1,0,0,1) | Quadratic index T(R) | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A4 · (1,0,0,1) | Reality type | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A4 · (1,0,0,1) | Conjugate highest weight | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A4 · (1,0,0,1) | Descends to the adjoint global form | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A4 · (1,0,0,1) | Order of central kernel | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A4 · (1,0,0,1) | Highest weight and conventions | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A4 · (1,0,0,1) | Global form and center | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A4 · (1,0,0,1) | Use in a calculation | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| A4 · (1,0,0,1) | Representation domain | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| C2 · (1,0) | Definition | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| C2 · (1,0) | Complex dimension | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| C2 · (1,0) | Coefficient field | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| C2 · (1,0) | Quadratic Casimir C₂ | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| C2 · (1,0) | Quadratic index T(R) | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| C2 · (1,0) | Reality type | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| C2 · (1,0) | Conjugate highest weight | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| C2 · (1,0) | Descends to the adjoint global form | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| C2 · (1,0) | Order of central kernel | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| C2 · (1,0) | Highest weight and conventions | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| C2 · (1,0) | Global form and center | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| C2 · (1,0) | Use in a calculation | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| C2 · (1,0) | Representation domain | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| C2 · (0,1) | Definition | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| C2 · (0,1) | Complex dimension | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| C2 · (0,1) | Coefficient field | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| C2 · (0,1) | Quadratic Casimir C₂ | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| C2 · (0,1) | Quadratic index T(R) | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| C2 · (0,1) | Reality type | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| C2 · (0,1) | Conjugate highest weight | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| C2 · (0,1) | Descends to the adjoint global form | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| C2 · (0,1) | Order of central kernel | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| C2 · (0,1) | Highest weight and conventions | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| C2 · (0,1) | Global form and center | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| C2 · (0,1) | Use in a calculation | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| C2 · (0,1) | Representation domain | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D4 · (1,0,0,0) | Definition | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D4 · (1,0,0,0) | Complex dimension | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D4 · (1,0,0,0) | Coefficient field | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D4 · (1,0,0,0) | Quadratic Casimir C₂ | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D4 · (1,0,0,0) | Quadratic index T(R) | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D4 · (1,0,0,0) | Reality type | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D4 · (1,0,0,0) | Conjugate highest weight | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D4 · (1,0,0,0) | Descends to the adjoint global form | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D4 · (1,0,0,0) | Order of central kernel | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D4 · (1,0,0,0) | Highest weight and conventions | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D4 · (1,0,0,0) | Global form and center | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D4 · (1,0,0,0) | Use in a calculation | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D4 · (1,0,0,0) | Representation domain | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D4 · (0,0,1,0) | Definition | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D4 · (0,0,1,0) | Complex dimension | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D4 · (0,0,1,0) | Coefficient field | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D4 · (0,0,1,0) | Quadratic Casimir C₂ | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D4 · (0,0,1,0) | Quadratic index T(R) | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D4 · (0,0,1,0) | Reality type | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D4 · (0,0,1,0) | Conjugate highest weight | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D4 · (0,0,1,0) | Descends to the adjoint global form | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D4 · (0,0,1,0) | Order of central kernel | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D4 · (0,0,1,0) | Highest weight and conventions | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D4 · (0,0,1,0) | Global form and center | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D4 · (0,0,1,0) | Use in a calculation | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D4 · (0,0,1,0) | Representation domain | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D4 · (0,0,0,1) | Definition | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D4 · (0,0,0,1) | Complex dimension | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D4 · (0,0,0,1) | Coefficient field | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D4 · (0,0,0,1) | Quadratic Casimir C₂ | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D4 · (0,0,0,1) | Quadratic index T(R) | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D4 · (0,0,0,1) | Reality type | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D4 · (0,0,0,1) | Conjugate highest weight | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D4 · (0,0,0,1) | Descends to the adjoint global form | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D4 · (0,0,0,1) | Order of central kernel | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D4 · (0,0,0,1) | Highest weight and conventions | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D4 · (0,0,0,1) | Global form and center | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D4 · (0,0,0,1) | Use in a calculation | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D4 · (0,0,0,1) | Representation domain | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (1,0,0,0,0) | Definition | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (1,0,0,0,0) | Complex dimension | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (1,0,0,0,0) | Coefficient field | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (1,0,0,0,0) | Quadratic Casimir C₂ | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (1,0,0,0,0) | Quadratic index T(R) | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (1,0,0,0,0) | Reality type | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (1,0,0,0,0) | Conjugate highest weight | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (1,0,0,0,0) | Descends to the adjoint global form | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (1,0,0,0,0) | Order of central kernel | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (1,0,0,0,0) | Highest weight and conventions | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (1,0,0,0,0) | Global form and center | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (1,0,0,0,0) | Use in a calculation | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (1,0,0,0,0) | Representation domain | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (0,0,0,0,1) | Definition | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (0,0,0,0,1) | Complex dimension | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (0,0,0,0,1) | Coefficient field | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (0,0,0,0,1) | Quadratic Casimir C₂ | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (0,0,0,0,1) | Quadratic index T(R) | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (0,0,0,0,1) | Reality type | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (0,0,0,0,1) | Conjugate highest weight | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (0,0,0,0,1) | Descends to the adjoint global form | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (0,0,0,0,1) | Order of central kernel | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (0,0,0,0,1) | Highest weight and conventions | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (0,0,0,0,1) | Global form and center | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (0,0,0,0,1) | Use in a calculation | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (0,0,0,0,1) | Representation domain | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (0,0,0,1,0) | Definition | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (0,0,0,1,0) | Complex dimension | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (0,0,0,1,0) | Coefficient field | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (0,0,0,1,0) | Quadratic Casimir C₂ | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (0,0,0,1,0) | Quadratic index T(R) | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (0,0,0,1,0) | Reality type | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (0,0,0,1,0) | Conjugate highest weight | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (0,0,0,1,0) | Descends to the adjoint global form | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (0,0,0,1,0) | Order of central kernel | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (0,0,0,1,0) | Highest weight and conventions | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (0,0,0,1,0) | Global form and center | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (0,0,0,1,0) | Use in a calculation | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (0,0,0,1,0) | Representation domain | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (0,1,0,0,0) | Definition | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (0,1,0,0,0) | Complex dimension | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (0,1,0,0,0) | Coefficient field | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (0,1,0,0,0) | Quadratic Casimir C₂ | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (0,1,0,0,0) | Quadratic index T(R) | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (0,1,0,0,0) | Reality type | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (0,1,0,0,0) | Conjugate highest weight | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (0,1,0,0,0) | Descends to the adjoint global form | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (0,1,0,0,0) | Order of central kernel | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (0,1,0,0,0) | Highest weight and conventions | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (0,1,0,0,0) | Global form and center | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (0,1,0,0,0) | Use in a calculation | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| D5 · (0,1,0,0,0) | Representation domain | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| G2 · (1,0) | Definition | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| G2 · (1,0) | Complex dimension | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| G2 · (1,0) | Coefficient field | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| G2 · (1,0) | Quadratic Casimir C₂ | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| G2 · (1,0) | Quadratic index T(R) | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| G2 · (1,0) | Reality type | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| G2 · (1,0) | Conjugate highest weight | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| G2 · (1,0) | Descends to the adjoint global form | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| G2 · (1,0) | Order of central kernel | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| G2 · (1,0) | Highest weight and conventions | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| G2 · (1,0) | Global form and center | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| G2 · (1,0) | Use in a calculation | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| G2 · (1,0) | Representation domain | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| G2 · (0,1) | Definition | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| G2 · (0,1) | Complex dimension | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| G2 · (0,1) | Coefficient field | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| G2 · (0,1) | Quadratic Casimir C₂ | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| G2 · (0,1) | Quadratic index T(R) | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| G2 · (0,1) | Reality type | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| G2 · (0,1) | Conjugate highest weight | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| G2 · (0,1) | Descends to the adjoint global form | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| G2 · (0,1) | Order of central kernel | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| G2 · (0,1) | Highest weight and conventions | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| G2 · (0,1) | Global form and center | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| G2 · (0,1) | Use in a calculation | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| G2 · (0,1) | Representation domain | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| F4 · (0,0,0,1) | Definition | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| F4 · (0,0,0,1) | Complex dimension | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| F4 · (0,0,0,1) | Coefficient field | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| F4 · (0,0,0,1) | Quadratic Casimir C₂ | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| F4 · (0,0,0,1) | Quadratic index T(R) | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| F4 · (0,0,0,1) | Reality type | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| F4 · (0,0,0,1) | Conjugate highest weight | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| F4 · (0,0,0,1) | Descends to the adjoint global form | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| F4 · (0,0,0,1) | Order of central kernel | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| F4 · (0,0,0,1) | Highest weight and conventions | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| F4 · (0,0,0,1) | Global form and center | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| F4 · (0,0,0,1) | Use in a calculation | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| F4 · (0,0,0,1) | Representation domain | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| F4 · (1,0,0,0) | Definition | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| F4 · (1,0,0,0) | Complex dimension | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| F4 · (1,0,0,0) | Coefficient field | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| F4 · (1,0,0,0) | Quadratic Casimir C₂ | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| F4 · (1,0,0,0) | Quadratic index T(R) | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| F4 · (1,0,0,0) | Reality type | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| F4 · (1,0,0,0) | Conjugate highest weight | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| F4 · (1,0,0,0) | Descends to the adjoint global form | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| F4 · (1,0,0,0) | Order of central kernel | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| F4 · (1,0,0,0) | Highest weight and conventions | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| F4 · (1,0,0,0) | Global form and center | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| F4 · (1,0,0,0) | Use in a calculation | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| F4 · (1,0,0,0) | Representation domain | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E6 · (1,0,0,0,0,0) | Definition | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E6 · (1,0,0,0,0,0) | Complex dimension | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E6 · (1,0,0,0,0,0) | Coefficient field | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E6 · (1,0,0,0,0,0) | Quadratic Casimir C₂ | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E6 · (1,0,0,0,0,0) | Quadratic index T(R) | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E6 · (1,0,0,0,0,0) | Reality type | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E6 · (1,0,0,0,0,0) | Conjugate highest weight | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E6 · (1,0,0,0,0,0) | Descends to the adjoint global form | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E6 · (1,0,0,0,0,0) | Order of central kernel | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E6 · (1,0,0,0,0,0) | Highest weight and conventions | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E6 · (1,0,0,0,0,0) | Global form and center | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E6 · (1,0,0,0,0,0) | Use in a calculation | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E6 · (1,0,0,0,0,0) | Representation domain | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E6 · (0,1,0,0,0,0) | Definition | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E6 · (0,1,0,0,0,0) | Complex dimension | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E6 · (0,1,0,0,0,0) | Coefficient field | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E6 · (0,1,0,0,0,0) | Quadratic Casimir C₂ | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E6 · (0,1,0,0,0,0) | Quadratic index T(R) | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E6 · (0,1,0,0,0,0) | Reality type | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E6 · (0,1,0,0,0,0) | Conjugate highest weight | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E6 · (0,1,0,0,0,0) | Descends to the adjoint global form | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E6 · (0,1,0,0,0,0) | Order of central kernel | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E6 · (0,1,0,0,0,0) | Highest weight and conventions | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E6 · (0,1,0,0,0,0) | Global form and center | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E6 · (0,1,0,0,0,0) | Use in a calculation | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E6 · (0,1,0,0,0,0) | Representation domain | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E7 · (0,0,0,0,0,0,1) | Definition | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E7 · (0,0,0,0,0,0,1) | Complex dimension | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E7 · (0,0,0,0,0,0,1) | Coefficient field | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E7 · (0,0,0,0,0,0,1) | Quadratic Casimir C₂ | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E7 · (0,0,0,0,0,0,1) | Quadratic index T(R) | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E7 · (0,0,0,0,0,0,1) | Reality type | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E7 · (0,0,0,0,0,0,1) | Conjugate highest weight | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E7 · (0,0,0,0,0,0,1) | Descends to the adjoint global form | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E7 · (0,0,0,0,0,0,1) | Order of central kernel | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E7 · (0,0,0,0,0,0,1) | Highest weight and conventions | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E7 · (0,0,0,0,0,0,1) | Global form and center | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E7 · (0,0,0,0,0,0,1) | Use in a calculation | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E7 · (0,0,0,0,0,0,1) | Representation domain | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E7 · (1,0,0,0,0,0,0) | Definition | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E7 · (1,0,0,0,0,0,0) | Complex dimension | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E7 · (1,0,0,0,0,0,0) | Coefficient field | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E7 · (1,0,0,0,0,0,0) | Quadratic Casimir C₂ | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E7 · (1,0,0,0,0,0,0) | Quadratic index T(R) | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E7 · (1,0,0,0,0,0,0) | Reality type | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E7 · (1,0,0,0,0,0,0) | Conjugate highest weight | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E7 · (1,0,0,0,0,0,0) | Descends to the adjoint global form | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E7 · (1,0,0,0,0,0,0) | Order of central kernel | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E7 · (1,0,0,0,0,0,0) | Highest weight and conventions | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E7 · (1,0,0,0,0,0,0) | Global form and center | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E7 · (1,0,0,0,0,0,0) | Use in a calculation | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E7 · (1,0,0,0,0,0,0) | Representation domain | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E8 · (0,0,0,0,0,0,0,1) | Definition | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E8 · (0,0,0,0,0,0,0,1) | Complex dimension | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E8 · (0,0,0,0,0,0,0,1) | Coefficient field | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E8 · (0,0,0,0,0,0,0,1) | Quadratic Casimir C₂ | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E8 · (0,0,0,0,0,0,0,1) | Quadratic index T(R) | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E8 · (0,0,0,0,0,0,0,1) | Reality type | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E8 · (0,0,0,0,0,0,0,1) | Conjugate highest weight | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E8 · (0,0,0,0,0,0,0,1) | Descends to the adjoint global form | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E8 · (0,0,0,0,0,0,0,1) | Order of central kernel | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E8 · (0,0,0,0,0,0,0,1) | Highest weight and conventions | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E8 · (0,0,0,0,0,0,0,1) | Global form and center | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E8 · (0,0,0,0,0,0,0,1) | Use in a calculation | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |
| E8 · (0,0,0,0,0,0,0,1) | Representation domain | Sections 25.3–25.4, 28.1–28.4: characters, Casimir eigenvalues, Weyl dimensions and type-A representations. |