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

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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.