A unipotent support for irreducible representations
type: Item
instance of: scholarly article
title: A unipotent support for irreducible representations
zbMATH Open document ID: 0789.20042
DOI: 10.1016/0001-8708(92)90035-J
author: G. Lusztig
published in: Advances in Mathematics
publication date: 1993-01-17T00:00:00Z
review text: In this paper the author solves Problem II from his earlier work [Proc. Symp. Pure Math. 37, 313-317 (1980; Zbl 0453.20005)]. This problem has to do with the existence (and uniqueness) of a certain unipotent class in a connected algebraic group \(G\) associated with an irreducible complex character of \(G(\mathbf{F}_ q)\). This class is called the unipotent class for the character. In the paper two other maps from the set of irreducible representations of \(G(\mathbf{F}_ q)\) to unipotent classes in \(G\) are studied, namely the one defined by the author himself in his book [Characters of reductive groups over a finite field, Ann. Math. Stud. 107, Princeton (1984; Zbl 0556.20033)] and the so-called wavefront set proposed by \textit{N. Kawanaka} [see e.g. Invent. Math. 84, 575-616 (1986; Zbl 0596.20028)]. Kawanaka has conjectured (and proved in certain cases) that these two maps coincide. One of the results in the paper under review establishes this conjecture in general. The main tool in the paper is a decomposition theorem for the character of a generalized Gelfand-Graev representation in terms of certain intersection cohomology complexes. This is also used to prove a result stated in another paper by the author [J. Fac. Sci., Univ. Tokyo, Sect. IA 36, 297-328 (1989; Zbl 0688.20020)] on the support of character sheaves.
reviewed by: Henning Haahr Andersen
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 20G40
Mathematics Subject Classification ID: 55N33
Mathematics Subject Classification ID: 20C33
zbMATH DE Number: 97609
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: connected algebraic group
zbMATH Keywords: irreducible complex character
zbMATH Keywords: irreducible representations
zbMATH Keywords: unipotent classes
zbMATH Keywords: wavefront set
zbMATH Keywords: generalized Gelfand-Graev representation
zbMATH Keywords: intersection cohomology complexes
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 97609