## Osaka Journal of Mathematics

### On the unipotent support of character sheaves

#### 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).

#### Article information

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

Dates
First available in Project Euclid: 17 September 2008

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1221656655

Mathematical Reviews number (MathSciNet)
MR2468596

Zentralblatt MATH identifier
1170.20028

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

#### Citation

Geck, Meinolf; Hézard, David. On the unipotent support of character sheaves. Osaka J. Math. 45 (2008), no. 3, 819--831. https://projecteuclid.org/euclid.ojm/1221656655

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