On the unipotent support of character sheaves

2007/10/01 by Meinolf Geck, Geck, Meinolf, David Hézard +1
Mathematics · #20C15 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.0710.0296

openalex publication_date 2007/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \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 \Z-basis of the \Z-module of unipotently supported virtual characters of G(F_q) (Kawanaka's conjecture).

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