A skein-like multiplication algorithm for unipotent Hecke algebras

Thiem, Nathaniel

doi:10.1090/S0002-9947-06-04052-9

A skein-like multiplication algorithm for unipotent Hecke algebras
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by Nathaniel Thiem PDF

Trans. Amer. Math. Soc. 359 (2007), 1685-1724 Request permission

Abstract:

Let $G$ be a finite group of Lie type (e.g. $GL_n(\mathbb {F}_q)$) and $U$ a maximal unipotent subgroup of $G$. If $\psi$ is a linear character of $U$, then the unipotent Hecke algebra is $\mathcal {H}_\psi =\mathrm {End}_{\mathbb {C}G} (\mathrm {Ind}_U^G(\psi ))$. Unipotent Hecke algebras have a natural basis coming from double cosets of $U$ in $G$. This paper describes relations for reducing products of basis elements, and gives a detailed description of the implications in the case $G=GL_n(\mathbb {F}_q)$.

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