On the unipotent support of character sheaves

Meinolf Geck, David Hezard

Research output: Contribution to journalArticle

4 Citations (Scopus)

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 languageEnglish
Pages (from-to)819-831
Number of pages13
JournalOsaka Journal of Mathematics
Volume45
Issue number3
Publication statusPublished - Sep 2008

Fingerprint

Sheaves
Z-module
Character Theory
Virtual Characters
Local System
Reductive Group
Finite Group
Restriction
Zero
Character

Keywords

  • reductive groups
  • lie type
  • representations

Cite this

Geck, M., & Hezard, D. (2008). On the unipotent support of character sheaves. Osaka Journal of Mathematics, 45(3), 819-831.

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

In: Osaka Journal of Mathematics, Vol. 45, No. 3, 09.2008, p. 819-831.

Research output: Contribution to journalArticle

Geck, M & Hezard, D 2008, 'On the unipotent support of character sheaves', Osaka Journal of Mathematics, vol. 45, no. 3, pp. 819-831.
Geck, Meinolf ; Hezard, David. / On the unipotent support of character sheaves. In: Osaka Journal of Mathematics. 2008 ; Vol. 45, No. 3. pp. 819-831.
@article{834975a3aa4e401c9ef2e4448dc63809,
title = "On the unipotent support of character sheaves",
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).",
keywords = "reductive groups, lie type, representations",
author = "Meinolf Geck and David Hezard",
year = "2008",
month = "9",
language = "English",
volume = "45",
pages = "819--831",
journal = "Osaka Journal of Mathematics",
issn = "0030-6126",
publisher = "Osaka University",
number = "3",

}

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 -