Semisimplicity of exterior powers of semisimple representations of groups
type: Item
instance of: scholarly article
title: Semisimplicity of exterior powers of semisimple representations of groups
zbMATH Open document ID: 0971.20005
author: George McNinch
published in: Journal of Algebra
publication date: 2001-07-11T00:00:00Z
review text: Let \(G\) be a group and \(K\) a field of characteristic \(p>0\). Let \(V=(V_1,\dots,V_s)\) be a sequence of semisimple representations of \(G\), and let \(m_1,\dots,m_s\) be integers satisfying \(1\leq m_i\leq\dim_KV_i=n_i\) for each \(i\). The author proves that if \(\sum_Im_i(n_i-m_i)<p\), then \(\bigvee^{m_1}V_1\otimes_K\cdots\otimes_K\bigvee^{m_s}V_s\) is semisimple. The proof is based on the reduction to the case when \(G\) is a simply connected and quasisimple linear algebraic group. This result gives an affirmative answer to a problem of J.-P.~Serre.
reviewed by: Andrei Marcus
Mathematics Subject Classification ID: 20C07
Mathematics Subject Classification ID: 16D60
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 20G05
zbMATH DE Number: 1429462
zbMATH Keywords: semisimple representations
zbMATH Keywords: exterior powers
zbMATH Keywords: linear algebraic groups
MaRDI profile type: Publication
full work available at URL: jabr.1999.8132
OpenAlex ID: W1993623327
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DOI: 10.1006/JABR.1999.8132
description: scientific article; zbMATH DE number 1429462