On the behavior of elements of prime order from Singer cycles in representations of special linear groups.
type: Item
instance of: scholarly article
title: On the behavior of elements of prime order from Singer cycles in representations of special linear groups.
zbMATH Open document ID: 1315.20043
DOI: 10.1134/S0081543814050113
author: Anna A. Osinovskaya
author: Anatoli Kondrat'ev
author: I. D. Suprunenko
published in: Proceedings of the Steklov Institute of Mathematics
publication date: 2014-11-13T00:00:00Z
review text: Let \(G=SL_n(q)\), where \(n\geq 2\) and \(q\) is a power of a prime \(p\). A Singer cycle of the group \(G\) is a cyclic subgroup of order \((q^n-1)/(q-1)\). In this paper, the authors study the problem of classifying irreducible \(G\)-modules over a field of characteristic \(p\) where an element of fixed prime order \(m\) from a Singer cycle of \(G\) acts freely in the following three cases: (a) the residue of \(q\) modulo \(m\) generates the multiplicative group of the field of order \(m\) (in particular, this holds for \(m=3\)); (b) \(m=5\); (c) \(n=2\).
reviewed by: Nan Ji-Zhu
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 20C33
zbMATH DE Number: 6369311
zbMATH Keywords: special linear groups
zbMATH Keywords: Singer cycles
zbMATH Keywords: absolutely irreducible modules
zbMATH Keywords: free actions of elements
zbMATH Keywords: fixed point free actions
zbMATH Keywords: representations of algebraic groups
zbMATH Keywords: finite groups of Lie type
MaRDI profile type: Publication
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full work available at URL: s0081543814050113
OpenAlex ID: W1988295111
description: scientific article; zbMATH DE number 6369311