Schur-Weyl reciprocity for the q-analogue of the alternating group

Details Schur-Weyl reciprocity for the q-analogue of the alternating group Schur-Weyl reciprocity for the q-analogue of the alternating group

2006-01-25

arxiv.org/abs/math/0601607v1

Mathematics

Representation Theory

24 pages

Scientific paper

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.

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