Osaka Journal of Mathematics

On the unipotent support of character sheaves

Meinolf Geck and David Hézard

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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).

Article information

Osaka J. Math., Volume 45, Number 3 (2008), 819-831.

First available in Project Euclid: 17 September 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20C15: Ordinary representations and characters
Secondary: 20G40: Linear algebraic groups over finite fields


Geck, Meinolf; Hézard, David. On the unipotent support of character sheaves. Osaka J. Math. 45 (2008), no. 3, 819--831.

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