### Abstract

Let G be a connected reductive group over 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(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 Z-basis of the Z-module of unipotently supported virtual characters of G(F-q) (Kawanaka's conjecture).

Original language | English |
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Pages (from-to) | 819-831 |

Number of pages | 13 |

Journal | Osaka Journal of Mathematics |

Volume | 45 |

Issue number | 3 |

Publication status | Published - Sep 2008 |

### Keywords

- reductive groups
- lie type
- representations

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## Cite this

Geck, M., & Hezard, D. (2008). On the unipotent support of character sheaves.

*Osaka Journal of Mathematics*,*45*(3), 819-831. http://projecteuclid.org/euclid.ojm/1221656655