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

Andrew Jones; Maxim Nazarov

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

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arxiv q-alg/9712041 v4 pith:LNWZE75S submitted 1997-12-16 q-alg math.QA

Andrew Jones , Maxim Nazarov This is my paper · ORCID

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abstract

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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Higher-level degenerate spin affine Hecke superalgebras
math.RT 2026-07 accept novelty 5.5 of 10

Higher-level degenerate spin affine Hecke superalgebras are isomorphic (after Clifford tensor) to higher-level degenerate affine Hecke–Clifford superalgebras, hence Morita superequivalent.

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