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49finite group records41Lie group records38Lie algebras22specified maps

62 released records. Individual groups and parameterized families are counted separately.

Mathematical records
ObjectKindEssential dataCoverage
C3:1C_3:\quad \mathbf{1}
C₃ irreducible representation 1
Representation
Finite
dimℂ 1executable
1 linked workbench
C3:χC_3:\quad \chi
C₃ irreducible representation χ
Representation
Finite
dimℂ 1executable
1 linked workbench
C3:χ2C_3:\quad \chi^2
C₃ irreducible representation χ²
Representation
Finite
dimℂ 1executable
1 linked workbench
S3:1S_3:\quad \mathbf{1}
S₃ irreducible representation 1
Representation
Finite
dimℂ 1executable
1 linked workbench
S3:sgnS_3:\quad \mathrm{sgn}
S₃ irreducible representation sgn
Representation
Finite
dimℂ 1executable
1 linked workbench
S3:2S_3:\quad \mathbf{2}
S₃ irreducible representation 2
Representation
Finite
dimℂ 2executable
1 linked workbench
D8:1D_8:\quad \mathbf{1}
D₈ irreducible representation 1
Representation
Finite
dimℂ 1executable
1 linked workbench
D8:aD_8:\quad a
D₈ irreducible representation a
Representation
Finite
dimℂ 1executable
1 linked workbench
D8:bD_8:\quad b
D₈ irreducible representation b
Representation
Finite
dimℂ 1executable
1 linked workbench
D8:cD_8:\quad c
D₈ irreducible representation c
Representation
Finite
dimℂ 1executable
1 linked workbench
D8:2D_8:\quad \mathbf{2}
D₈ irreducible representation 2
Representation
Finite
dimℂ 2executable
1 linked workbench
Q8:1Q_8:\quad \mathbf{1}
Q₈ irreducible representation 1
Representation
Finite
dimℂ 1executable
1 linked workbench
Q8:aQ_8:\quad a
Q₈ irreducible representation a
Representation
Finite
dimℂ 1executable
1 linked workbench
Q8:bQ_8:\quad b
Q₈ irreducible representation b
Representation
Finite
dimℂ 1executable
1 linked workbench
Q8:cQ_8:\quad c
Q₈ irreducible representation c
Representation
Finite
dimℂ 1executable
1 linked workbench
Q8:2Q_8:\quad \mathbf{2}
Q₈ irreducible representation 2
Representation
Finite
dimℂ 2executable
1 linked workbench
A4:1A_4:\quad \mathbf{1}
A₄ irreducible representation 1
Representation
Finite
dimℂ 1executable
1 linked workbench
A4:1′A_4:\quad \mathbf{1}'
A₄ irreducible representation 1′
Representation
Finite
dimℂ 1executable
1 linked workbench
A4:1′′A_4:\quad \mathbf{1}''
A₄ irreducible representation 1″
Representation
Finite
dimℂ 1executable
1 linked workbench
A4:3A_4:\quad \mathbf{3}
A₄ irreducible representation 3
Representation
Finite
dimℂ 3executable
1 linked workbench
S4:1S_4:\quad \mathbf{1}
S₄ irreducible representation 1
Representation
Finite
dimℂ 1executable
1 linked workbench
S4:sgnS_4:\quad \mathrm{sgn}
S₄ irreducible representation sgn
Representation
Finite
dimℂ 1executable
1 linked workbench
S4:2S_4:\quad \mathbf{2}
S₄ irreducible representation 2
Representation
Finite
dimℂ 2executable
1 linked workbench
S4:3S_4:\quad \mathbf{3}
S₄ irreducible representation 3
Representation
Finite
dimℂ 3executable
1 linked workbench
S4:3′S_4:\quad \mathbf{3}'
S₄ irreducible representation 3′
Representation
Finite
dimℂ 3executable
1 linked workbench
A5:1A_5:\quad \mathbf{1}
A₅ irreducible representation 1
Representation
Finite
dimℂ 1executable
1 linked workbench
A5:3A_5:\quad \mathbf{3}
A₅ irreducible representation 3
Representation
Finite
dimℂ 3executable
1 linked workbench
A5:3′A_5:\quad \mathbf{3}'
A₅ irreducible representation 3′
Representation
Finite
dimℂ 3executable
1 linked workbench
A5:4A_5:\quad \mathbf{4}
A₅ irreducible representation 4
Representation
Finite
dimℂ 4executable
1 linked workbench
A5:5A_5:\quad \mathbf{5}
A₅ irreducible representation 5
Representation
Finite
dimℂ 5executable
1 linked workbench
A1:V(1)A_{1}:\quad V_{(1)}
Doublet of SU(2)
Representation
Lie theory
dimℂ 2executable
2 linked workbenchs
A1:V(2)A_{1}:\quad V_{(2)}
Adjoint of SU(2)
Representation
Lie theory
dimℂ 3executable
2 linked workbenchs
A2:V(1,0)A_{2}:\quad V_{(1,0)}
Fundamental of SU(3)
Representation
Lie theory
dimℂ 3executable
5 linked workbenchs
A2:V(0,1)A_{2}:\quad V_{(0,1)}
Conjugate fundamental of SU(3)
Representation
Lie theory
dimℂ 3executable
5 linked workbenchs
A2:V(1,1)A_{2}:\quad V_{(1,1)}
Adjoint of SU(3)
Representation
Lie theory
dimℂ 8executable
5 linked workbenchs
A2:V(2,0)A_{2}:\quad V_{(2,0)}
Symmetric sextet of SU(3)
Representation
Lie theory
dimℂ 6executable
5 linked workbenchs
A2:V(3,0)A_{2}:\quad V_{(3,0)}
Decuplet of SU(3)
Representation
Lie theory
dimℂ 10executable
5 linked workbenchs
A2:V(2,2)A_{2}:\quad V_{(2,2)}
27-dimensional irrep of SU(3)
Representation
Lie theory
dimℂ 27executable
5 linked workbenchs
A3:V(1,0,0)A_{3}:\quad V_{(1,0,0)}
Fundamental of SU(4)
Representation
Lie theory
dimℂ 4executable
3 linked workbenchs
A3:V(0,1,0)A_{3}:\quad V_{(0,1,0)}
Two-index antisymmetric of SU(4)
Representation
Lie theory
dimℂ 6executable
3 linked workbenchs
A3:V(1,0,1)A_{3}:\quad V_{(1,0,1)}
Adjoint of SU(4)
Representation
Lie theory
dimℂ 15executable
3 linked workbenchs
A4:V(1,0,0,0)A_{4}:\quad V_{(1,0,0,0)}
Fundamental of SU(5)
Representation
Lie theory
dimℂ 5executable
3 linked workbenchs
A4:V(0,1,0,0)A_{4}:\quad V_{(0,1,0,0)}
Two-index antisymmetric of SU(5)
Representation
Lie theory
dimℂ 10executable
3 linked workbenchs
A4:V(1,0,0,1)A_{4}:\quad V_{(1,0,0,1)}
Adjoint of SU(5)
Representation
Lie theory
dimℂ 24executable
3 linked workbenchs
C2:V(1,0)C_{2}:\quad V_{(1,0)}
Defining representation of Sp(2) = USp(4)
Representation
Lie theory
dimℂ 4executable
1 linked workbench
C2:V(0,1)C_{2}:\quad V_{(0,1)}
Five-dimensional irrep of Sp(2) = USp(4)
Representation
Lie theory
dimℂ 5executable
1 linked workbench
D4:V(1,0,0,0)D_{4}:\quad V_{(1,0,0,0)}
Vector of Spin(8)
Representation
Lie theory
dimℂ 8executable
1 linked workbench
D4:V(0,0,1,0)D_{4}:\quad V_{(0,0,1,0)}
Half-spin representation of Spin(8)
Representation
Lie theory
dimℂ 8executable
1 linked workbench
D4:V(0,0,0,1)D_{4}:\quad V_{(0,0,0,1)}
Other half-spin representation of Spin(8)
Representation
Lie theory
dimℂ 8executable
1 linked workbench
D5:V(1,0,0,0,0)D_{5}:\quad V_{(1,0,0,0,0)}
Vector of Spin(10)
Representation
Lie theory
dimℂ 10executable
1 linked workbench
D5:V(0,0,0,0,1)D_{5}:\quad V_{(0,0,0,0,1)}
Chiral spinor of Spin(10)
Representation
Lie theory
dimℂ 16executable
1 linked workbench
D5:V(0,0,0,1,0)D_{5}:\quad V_{(0,0,0,1,0)}
Conjugate chiral spinor of Spin(10)
Representation
Lie theory
dimℂ 16executable
1 linked workbench
D5:V(0,1,0,0,0)D_{5}:\quad V_{(0,1,0,0,0)}
Adjoint of Spin(10)
Representation
Lie theory
dimℂ 45executable
1 linked workbench
G2:V(1,0)G_{2}:\quad V_{(1,0)}
Fundamental of G2 (compact)
Representation
Lie theory
dimℂ 7executable
1 linked workbench
G2:V(0,1)G_{2}:\quad V_{(0,1)}
Adjoint of G2 (compact)
Representation
Lie theory
dimℂ 14executable
1 linked workbench
F4:V(0,0,0,1)F_{4}:\quad V_{(0,0,0,1)}
Minimal representation of F4 (compact)
Representation
Lie theory
dimℂ 26executable
1 linked workbench
F4:V(1,0,0,0)F_{4}:\quad V_{(1,0,0,0)}
Adjoint of F4 (compact)
Representation
Lie theory
dimℂ 52executable
1 linked workbench
E6:V(1,0,0,0,0,0)E_{6}:\quad V_{(1,0,0,0,0,0)}
27-dimensional representation of E6 (compact simply connected)
Representation
Lie theory
dimℂ 27executable
1 linked workbench
E6:V(0,1,0,0,0,0)E_{6}:\quad V_{(0,1,0,0,0,0)}
Adjoint of E6 (compact simply connected)
Representation
Lie theory
dimℂ 78executable
1 linked workbench
E7:V(0,0,0,0,0,0,1)E_{7}:\quad V_{(0,0,0,0,0,0,1)}
56-dimensional representation of E7 (compact simply connected)
Representation
Lie theory
dimℂ 56executable
1 linked workbench
E7:V(1,0,0,0,0,0,0)E_{7}:\quad V_{(1,0,0,0,0,0,0)}
Adjoint of E7 (compact simply connected)
Representation
Lie theory
dimℂ 133executable
1 linked workbench
E8:V(0,0,0,0,0,0,0,1)E_{8}:\quad V_{(0,0,0,0,0,0,0,1)}
Adjoint of E8 (compact simply connected)
Representation
Lie theory
dimℂ 248executable
1 linked workbench
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Finite-simple classificationLie classification