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The $$q$$-analogue of the alternating group and its representations. (English) Zbl 1046.20010
Summary: We define a new algebra. This algebra has a parameter $$q$$. The defining relations of this algebra at $$q=1$$ coincide with the basic relations of the alternating group. We also give a new subalgebra of the Hecke algebra of type $$A$$ which is isomorphic to this algebra. This algebra is free of rank half that of the Hecke algebra. Hence this algebra is regarded as a $$q$$-analogue of the alternating group.
All the isomorphism classes of the irreducible representations of this algebra and the $$q$$-analogue of the branching rule between the symmetric group and the alternating group are obtained.

MSC:
 20C30 Representations of finite symmetric groups 20C08 Hecke algebras and their representations 20C15 Ordinary representations and characters
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References:
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