Hideo Mitsuhashi
Published 2006-01-25Version 1
We establish Schur-Weyl reciprocity for the q-analogue of the alternating group. We analyze the sign q-permutation representation of the Hecke algebra on the tensor product of the super vector space V in detail, and examine its restriction to the q-analogue of the alternating group. In consequence, we find out that if the dimensions of even part and odd part of V are same, then the centralizer of the q-analogue of the alternating group is a Z_2-crossed product of the centralizer of the Hecke algebra and obtain Schur-Weyl reciprocity between them. Though the structure of the centralizer is more complicated for the general case, we obtained some results about the case.
Centralizers in the Hecke algebras of complex reflection groups
A categorification of Hecke algebras with parameters 1 and v
The $p$-Canonical Basis for Hecke Algebras
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