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02 November 2024
 
  » arxiv » 0710.0296

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On the unipotent support of character sheave
Meinolf Geck ; David Hézard ;
Date 1 Oct 2007
AbstractLet $G$ 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 {em 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 {em 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 $$-basis of the $$-module of unipotently supported virtual characters of $G(F_q)$ (Kawanaka’s conjecture).
Source arXiv, 0710.0296
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