dorsal/arxiv
View SchemaAffine Sergeev Algebra and $q$-Analogues of the Young Symmetrizers for Projective Representations of the Symmetric Group
| Authors | Andrew Jones, Maxim Nazarov |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9712041 |
| URL | https://arxiv.org/abs/q-alg/9712041 |
| Journal | Proc. London Math. Soc. 78 (1999), 481-512 |
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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"abstract": "We study a $q$-deformation for the semi-direct product of the symmetric group\n$S_n$ with the Clifford algebra on $n$ anticommuting generators. We obtain a\n$q$-version of the projective analogue for the classical Young symmetrizer\nfound by the second author [Adv. Math. 127(1997), 190-257]. Our main tool is an\nanalogue of the Hecke algebra of complex valued functions on the group $GL_{n}$\nover a $p$-adic field relative to the Iwahori subgroup.",
"arxiv_id": "q-alg/9712041",
"authors": [
"Andrew Jones",
"Maxim Nazarov"
],
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"q-alg",
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"journal_ref": "Proc. London Math. Soc. 78 (1999), 481-512",
"title": "Affine Sergeev Algebra and $q$-Analogues of the Young Symmetrizers for Projective Representations of the Symmetric Group",
"url": "https://arxiv.org/abs/q-alg/9712041"
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