Finite fields, root systems, and orbit numbers of Chevalley groups
type: Item
instance of: scholarly article
title: Finite fields, root systems, and orbit numbers of Chevalley groups
zbMATH Open document ID: 0905.20002
author: Peter Fleischmann
published in: Finite Fields and their Applications
publication date: 1999-02-02T00:00:00Z
review text: Let \(G\) be a finite group of Lie type. \textit{G. Lusztig} [Characters of reductive groups over a finite field (1984; Zbl 0556.20033)] gave a parametrization of the characters in \(\text{Irr}_{\overline\mathbb{Q}_\ell}(G^*)\), where \(\overline\mathbb{Q}_\ell\) is the algebraic closure of the \(\ell\)-adic rationals and \(\ell\) is a prime different from the defining characteristic. In case the algebraic group \({\mathbf G}^*\) of \(G\) has connected centre (such as \(\text{SL}_n(q)\), \(\text{PGL}_n(q)\)), this parametrization is given in terms of irreducible unipotent characters of the centralizers \(G_s\) of the semisimple conjugacy classes \([S]\) of \(G\). The paper under review describes a combinatorial technique to determine the number of semisimple conjugacy classes and adjoint orbits with fixed class of centralizers for simply connected finite groups of Lie type.
Mathematics Subject Classification ID: 20C33
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 05C15
Mathematics Subject Classification ID: 20G40
zbMATH DE Number: 1199986
zbMATH Keywords: finite groups of Lie type
zbMATH Keywords: irreducible unipotent characters
zbMATH Keywords: centralizers
zbMATH Keywords: semisimple conjugacy classes
zbMATH Keywords: adjoint orbits
reviewed by: Ahmed A. Khammash
MaRDI profile type: Publication
OpenAlex ID: W2014345745
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DOI: 10.1006/FFTA.1996.0171
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description: scientific article; zbMATH DE number 1199986