Generic patterns for extensions of simple modules for finite Chevalley groups
type: Item
instance of: scholarly article
title: Generic patterns for extensions of simple modules for finite Chevalley groups
zbMATH Open document ID: 0929.20037
author: Cornelius Pillen
published in: Journal of Algebra
publication date: 1999-11-07T00:00:00Z
review text: Let \(G\) be a semi-simple algebraic group over an algebraically closed field \(k\). Denote by \(G(n)\) the finite subgroup of \(G\) consisting of the points over the finite subfield of \(k\) with \(p^n\) elements. In this paper the author compares extensions between simple modules for \(G(n)\) with those of \(G\). (Recall that all simple \(G(n)\)-modules are restrictions of simple \(G\)-modules.) He proves that under certain generic assumptions on the highest weights involved, namely that these are ``deep enough'' inside their alcoves, any such non-trivial extension for \(G\) corresponding to \(n\)-restricted weights is also a non-trivial extension for \(G(n)\). The results extend the author's previous work [J. Algebra 189, No. 1, 101-124 (1997; see the preceding review Zbl 0929.20036)] and may also be considered as a continuation of the reviewer's paper [J. Algebra 111, 388-403 (1987; Zbl 0626.20029)].
reviewed by: Henning Haahr Andersen
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 20G40
Mathematics Subject Classification ID: 20C33
zbMATH DE Number: 1271814
zbMATH Keywords: extensions of simple modules
zbMATH Keywords: generic patterns
zbMATH Keywords: Chevalley groups
zbMATH Keywords: highest weights
MaRDI profile type: Publication
full work available at URL: jabr.1998.7639
OpenAlex ID: W2063233565
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DOI: 10.1006/JABR.1998.7639
description: scientific article; zbMATH DE number 1271814