A skein-like multiplication algorithm for unipotent Hecke algebras
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- by Nathaniel Thiem PDF
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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 $G=GL_n(\mathbb {F}_q)$.References
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Additional Information
- Nathaniel Thiem
- Affiliation: Department of Mathematics, Stanford University, Stanford, California 94305-2125
- Received by editor(s): June 15, 2004
- Received by editor(s) in revised form: January 21, 2005
- Published electronically: October 16, 2006
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2272146