On the unipotent support of character sheaves. (English) Zbl 1170.20028

Geck, Meinolf; Hézard, David

Osaka J. Math. 45, No. 3, 819-831 (2008).

Let \(G\) be a connected reductive group over \(\mathbb{F}_q\), where the center of \(G\) is connected and both \(q\) and the characteristic \(p\) are large enough. The authors show that under a certain technical condition, treated in the thesis of the second author, 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 \(\mathbb{Z}\)-basis of the \(\mathbb{Z}\)-module of unipotently supported virtual characters of \(G(\mathbb{F}_q)\) (Kawanaka’s conjecture).

Reviewer: Wilberd van der Kallen (Utrecht)

MSC:

20G05	Representation theory for linear algebraic groups
20G40	Linear algebraic groups over finite fields

Keywords:

connected reductive groups; character sheaves; unipotent support; generalized Gelfand-Graev characters; Springer correspondence; irreducible local systems; virtual characters

References:

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