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A skein-like multiplication algorithm for unipotent Hecke algebras


Author: Nathaniel Thiem
Journal: Trans. Amer. Math. Soc. 359 (2007), 1685-1724
MSC (2000): Primary 20C08; Secondary 05Exx
DOI: https://doi.org/10.1090/S0002-9947-06-04052-9
Published electronically: October 16, 2006
MathSciNet review: 2272146
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

Nathaniel Thiem
Affiliation: Department of Mathematics, Stanford University, Stanford, California 94305-2125

DOI: https://doi.org/10.1090/S0002-9947-06-04052-9
Keywords: Hecke algebra, Gelfand-Graev representation, unipotent Hecke algebra, Yokonuma Hecke algebra
Received by editor(s): June 15, 2004
Received by editor(s) in revised form: January 21, 2005
Published electronically: October 16, 2006
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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