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The q-Analogue of the Alternating Group and Its Representations

โœ Scribed by Hideo Mitsuhashi

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
175 KB
Volume
240
Category
Article
ISSN
0021-8693

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โœฆ Synopsis

We define the new algebra. This algebra has a parameter q. The defining relations of this algebra at q s 1 coincide with the basic relations of the alternating group. We also give the 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.

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