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gptkb:U(1)_×_U(1)
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all irreducible representations are 1-dimensional
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gptkb:Spin(3)
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quaternionic representations
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gptkb:GL(2,R)
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well-studied
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gptkb:sl(n,_C)
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well-studied
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gptkb:U(1)
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well understood
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gptkb:circle_group_S^1
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characters are integer powers
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gptkb:sl(2,_C)
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well-studied
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gptkb:GL(2,_ℂ)
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important in mathematics and physics
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gptkb:symmetric_group_S_N
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irreducible representations correspond to partitions of N
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gptkb:Symmetric_group
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well-studied
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gptkb:SU(2)_symmetry
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spin representations
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gptkb:GL(2,_R)
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well-studied
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gptkb:SU(2)_symmetry
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irreducible representations
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gptkb:Special_Orthogonal_Group_in_2_Dimensions
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characters are e^{inθ}
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gptkb:symmetric_group_S_n_(n_≥_3)
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irreducible representations correspond to partitions of n
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gptkb:S_7
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15 irreducible representations
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gptkb:symmetric_group_S_9
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30 irreducible representations
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gptkb:circle_group_SO(2)
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characters are e^{inθ}, n∈Z
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gptkb:GL(n,_F)
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well-studied
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gptkb:special_orthogonal_group_SO(2)
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all irreducible representations are 1-dimensional
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