Affine Sergeev Algebra and $q$-Analogues of the Young Symmetrizers for Projective Representations of the Symmetric Group

Details Affine Sergeev Algebra and $q$-Analogues of the Young Symmetrizers for Projective Representations of the Symmetric Group Affine Sergeev Algebra and $q$-Analogues of the Young Symmetrizers for Projective Representations of the Symmetric Group

1997-12-16

arxiv.org/abs/q-alg/9712041v4

Proc. London Math. Soc. 78 (1999), 481-512

Mathematics

Quantum Algebra

LaTeX, 28 pages

Scientific paper

We study a $q$-deformation for the semi-direct product of the symmetric group $S_n$ with the Clifford algebra on $n$ anticommuting generators. We obtain a $q$-version of the projective analogue for the classical Young symmetrizer found by the second author [Adv. Math. 127(1997), 190-257]. Our main tool is an analogue of the Hecke algebra of complex valued functions on the group $GL_{n}$ over a $p$-adic field relative to the Iwahori subgroup.

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