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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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