### Abstract

Original language | English |
---|---|

Pages (from-to) | 819-831 |

Number of pages | 13 |

Journal | Osaka Journal of Mathematics |

Volume | 45 |

Issue number | 3 |

Publication status | Published - Sep 2008 |

### Fingerprint

### Keywords

- reductive groups
- lie type
- representations

### Cite this

*Osaka Journal of Mathematics*,

*45*(3), 819-831.

**On the unipotent support of character sheaves.** / Geck, Meinolf; Hezard, David.

Research output: Contribution to journal › Article

*Osaka Journal of Mathematics*, vol. 45, no. 3, pp. 819-831.

}

TY - JOUR

T1 - On the unipotent support of character sheaves

AU - Geck, Meinolf

AU - Hezard, David

PY - 2008/9

Y1 - 2008/9

N2 - 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).

AB - 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).

KW - reductive groups

KW - lie type

KW - representations

M3 - Article

VL - 45

SP - 819

EP - 831

JO - Osaka Journal of Mathematics

JF - Osaka Journal of Mathematics

SN - 0030-6126

IS - 3

ER -