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September 2008 On the unipotent support of character sheaves
Meinolf Geck, David Hézard
Osaka J. Math. 45(3): 819-831 (September 2008).

Abstract

Let $G$ be a connected reductive group over $\mathbb{F}_{q}$, where $q$ is large enough and the center of $G$ is connected. We are concerned with Lusztig's theory of character sheaves, a geometric version of the classical character theory of the finite group $G(\mathbb{F}_{q})$. We show that under a certain technical condition, the restriction of a character sheaf to its unipotent support (as defined by Lusztig) is either zero or an irreducible local system. As an application, the generalized Gelfand-Graev characters are shown to form a $\mathbb{Z}$-basis of the $\mathbb{Z}$-module of unipotently supported virtual characters of $G(\mathbb{F}_{q})$ (Kawanaka's conjecture).

Citation

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Meinolf Geck. David Hézard. "On the unipotent support of character sheaves." Osaka J. Math. 45 (3) 819 - 831, September 2008.

Information

Published: September 2008
First available in Project Euclid: 17 September 2008

zbMATH: 1170.20028
MathSciNet: MR2468596

Subjects:
Primary: 20C15
Secondary: 20G40

Rights: Copyright © 2008 Osaka University and Osaka City University, Departments of Mathematics

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Vol.45 • No. 3 • September 2008
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