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49finite group records41Lie group records38Lie algebras22specified maps
62 released records. Individual groups and parameterized families are counted separately.
| Object | Kind | Essential data | Coverage |
|---|---|---|---|
| C₃ · 1 C₃ irreducible representation 1 | Representation Finite | dimℂ 1 | executable 1 linked workbench |
| C₃ · χ C₃ irreducible representation χ | Representation Finite | dimℂ 1 | executable 1 linked workbench |
| C₃ · χ² C₃ irreducible representation χ² | Representation Finite | dimℂ 1 | executable 1 linked workbench |
| S₃ · 1 S₃ irreducible representation 1 | Representation Finite | dimℂ 1 | executable 1 linked workbench |
| S₃ · sgn S₃ irreducible representation sgn | Representation Finite | dimℂ 1 | executable 1 linked workbench |
| S₃ · 2 S₃ irreducible representation 2 | Representation Finite | dimℂ 2 | executable 1 linked workbench |
| D₈ · 1 D₈ irreducible representation 1 | Representation Finite | dimℂ 1 | executable 1 linked workbench |
| D₈ · a D₈ irreducible representation a | Representation Finite | dimℂ 1 | executable 1 linked workbench |
| D₈ · b D₈ irreducible representation b | Representation Finite | dimℂ 1 | executable 1 linked workbench |
| D₈ · c D₈ irreducible representation c | Representation Finite | dimℂ 1 | executable 1 linked workbench |
| D₈ · 2 D₈ irreducible representation 2 | Representation Finite | dimℂ 2 | executable 1 linked workbench |
| Q₈ · 1 Q₈ irreducible representation 1 | Representation Finite | dimℂ 1 | executable 1 linked workbench |
| Q₈ · a Q₈ irreducible representation a | Representation Finite | dimℂ 1 | executable 1 linked workbench |
| Q₈ · b Q₈ irreducible representation b | Representation Finite | dimℂ 1 | executable 1 linked workbench |
| Q₈ · c Q₈ irreducible representation c | Representation Finite | dimℂ 1 | executable 1 linked workbench |
| Q₈ · 2 Q₈ irreducible representation 2 | Representation Finite | dimℂ 2 | executable 1 linked workbench |
| A₄ · 1 A₄ irreducible representation 1 | Representation Finite | dimℂ 1 | executable 1 linked workbench |
| A₄ · 1′ A₄ irreducible representation 1′ | Representation Finite | dimℂ 1 | executable 1 linked workbench |
| A₄ · 1″ A₄ irreducible representation 1″ | Representation Finite | dimℂ 1 | executable 1 linked workbench |
| A₄ · 3 A₄ irreducible representation 3 | Representation Finite | dimℂ 3 | executable 1 linked workbench |
| S₄ · 1 S₄ irreducible representation 1 | Representation Finite | dimℂ 1 | executable 1 linked workbench |
| S₄ · sgn S₄ irreducible representation sgn | Representation Finite | dimℂ 1 | executable 1 linked workbench |
| S₄ · 2 S₄ irreducible representation 2 | Representation Finite | dimℂ 2 | executable 1 linked workbench |
| S₄ · 3 S₄ irreducible representation 3 | Representation Finite | dimℂ 3 | executable 1 linked workbench |
| S₄ · 3′ S₄ irreducible representation 3′ | Representation Finite | dimℂ 3 | executable 1 linked workbench |
| A₅ · 1 A₅ irreducible representation 1 | Representation Finite | dimℂ 1 | executable 1 linked workbench |
| A₅ · 3 A₅ irreducible representation 3 | Representation Finite | dimℂ 3 | executable 1 linked workbench |
| A₅ · 3′ A₅ irreducible representation 3′ | Representation Finite | dimℂ 3 | executable 1 linked workbench |
| A₅ · 4 A₅ irreducible representation 4 | Representation Finite | dimℂ 4 | executable 1 linked workbench |
| A₅ · 5 A₅ irreducible representation 5 | Representation Finite | dimℂ 5 | executable 1 linked workbench |
| A1 · (1) Doublet of SU(2) | Representation Lie theory | dimℂ 2 | executable 2 linked workbenchs |
| A1 · (2) Adjoint of SU(2) | Representation Lie theory | dimℂ 3 | executable 2 linked workbenchs |
| A2 · (1,0) Fundamental of SU(3) | Representation Lie theory | dimℂ 3 | executable 5 linked workbenchs |
| A2 · (0,1) Conjugate fundamental of SU(3) | Representation Lie theory | dimℂ 3 | executable 5 linked workbenchs |
| A2 · (1,1) Adjoint of SU(3) | Representation Lie theory | dimℂ 8 | executable 5 linked workbenchs |
| A2 · (2,0) Symmetric sextet of SU(3) | Representation Lie theory | dimℂ 6 | executable 5 linked workbenchs |
| A2 · (3,0) Decuplet of SU(3) | Representation Lie theory | dimℂ 10 | executable 5 linked workbenchs |
| A2 · (2,2) 27-dimensional irrep of SU(3) | Representation Lie theory | dimℂ 27 | executable 5 linked workbenchs |
| A3 · (1,0,0) Fundamental of SU(4) | Representation Lie theory | dimℂ 4 | executable 3 linked workbenchs |
| A3 · (0,1,0) Two-index antisymmetric of SU(4) | Representation Lie theory | dimℂ 6 | executable 3 linked workbenchs |
| A3 · (1,0,1) Adjoint of SU(4) | Representation Lie theory | dimℂ 15 | executable 3 linked workbenchs |
| A4 · (1,0,0,0) Fundamental of SU(5) | Representation Lie theory | dimℂ 5 | executable 3 linked workbenchs |
| A4 · (0,1,0,0) Two-index antisymmetric of SU(5) | Representation Lie theory | dimℂ 10 | executable 3 linked workbenchs |
| A4 · (1,0,0,1) Adjoint of SU(5) | Representation Lie theory | dimℂ 24 | executable 3 linked workbenchs |
| C2 · (1,0) Defining representation of Sp(2) = USp(4) | Representation Lie theory | dimℂ 4 | executable 1 linked workbench |
| C2 · (0,1) Five-dimensional irrep of Sp(2) = USp(4) | Representation Lie theory | dimℂ 5 | executable 1 linked workbench |
| D4 · (1,0,0,0) Vector of Spin(8) | Representation Lie theory | dimℂ 8 | executable 1 linked workbench |
| D4 · (0,0,1,0) Half-spin representation of Spin(8) | Representation Lie theory | dimℂ 8 | executable 1 linked workbench |
| D4 · (0,0,0,1) Other half-spin representation of Spin(8) | Representation Lie theory | dimℂ 8 | executable 1 linked workbench |
| D5 · (1,0,0,0,0) Vector of Spin(10) | Representation Lie theory | dimℂ 10 | executable 1 linked workbench |
| D5 · (0,0,0,0,1) Chiral spinor of Spin(10) | Representation Lie theory | dimℂ 16 | executable 1 linked workbench |
| D5 · (0,0,0,1,0) Conjugate chiral spinor of Spin(10) | Representation Lie theory | dimℂ 16 | executable 1 linked workbench |
| D5 · (0,1,0,0,0) Adjoint of Spin(10) | Representation Lie theory | dimℂ 45 | executable 1 linked workbench |
| G2 · (1,0) Fundamental of G2 (compact) | Representation Lie theory | dimℂ 7 | executable 1 linked workbench |
| G2 · (0,1) Adjoint of G2 (compact) | Representation Lie theory | dimℂ 14 | executable 1 linked workbench |
| F4 · (0,0,0,1) Minimal representation of F4 (compact) | Representation Lie theory | dimℂ 26 | executable 1 linked workbench |
| F4 · (1,0,0,0) Adjoint of F4 (compact) | Representation Lie theory | dimℂ 52 | executable 1 linked workbench |
| E6 · (1,0,0,0,0,0) 27-dimensional representation of E6 (compact simply connected) | Representation Lie theory | dimℂ 27 | executable 1 linked workbench |
| E6 · (0,1,0,0,0,0) Adjoint of E6 (compact simply connected) | Representation Lie theory | dimℂ 78 | executable 1 linked workbench |
| E7 · (0,0,0,0,0,0,1) 56-dimensional representation of E7 (compact simply connected) | Representation Lie theory | dimℂ 56 | executable 1 linked workbench |
| E7 · (1,0,0,0,0,0,0) Adjoint of E7 (compact simply connected) | Representation Lie theory | dimℂ 133 | executable 1 linked workbench |
| E8 · (0,0,0,0,0,0,0,1) Adjoint of E8 (compact simply connected) | Representation Lie theory | dimℂ 248 | executable 1 linked workbench |
Coverage is specific. Classification identifies a mathematical object or family. Reference supplies stated properties. Executable links to a bounded calculation. Read the coverage policy.