Equidimensional representations of \(2\)-simple groups
type: Item
instance of: scholarly article
title: Equidimensional representations of \(2\)-simple groups
zbMATH Open document ID: 0820.20051
published in: Journal of Algebra
publication date: 1993-05-16T00:00:00Z
review text: Let \(G\) be a complex reduction algebraic group, \(\rho:G\to\text{GL}(V)\) a finite dimensional complex representation and \(\pi:V\to V//G\) the categorical quotient of the action of \(G\) on \(V\) induced by \(\rho\). There is the conjecture in invariant theory that if \(G\) is a connected semisimple group and \(\pi\) an equidimensional morphism, then \(V//G\) is smooth (and hence isomorphic to an affine space). This conjecture was formulated twenty years ago and since then has been verified for simple groups, for semisimple groups and their irreducible representations \(\rho\) (the verification followed a posteriori from the corresponding classification results) and for tori. In the present paper this conjecture is proved for a large class of the semisimple groups having exactly two simple factors (also in an a posteriori way, via classification of the equidimensional representations of these groups).
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 20G20
Mathematics Subject Classification ID: 14L30
Mathematics Subject Classification ID: 14L24
Mathematics Subject Classification ID: 14L35
zbMATH DE Number: 168592
zbMATH Keywords: complex reduction algebraic groups
zbMATH Keywords: complex representations
zbMATH Keywords: actions
zbMATH Keywords: invariant theory
zbMATH Keywords: connected semisimple groups
zbMATH Keywords: equidimensional morphisms
zbMATH Keywords: simple groups
zbMATH Keywords: irreducible representations
zbMATH Keywords: equidimensional representations
author: David Wehlau
reviewed by: Vladimir L. Popov
MaRDI profile type: Publication
full work available at URL: jabr.1993.1024
OpenAlex ID: W2011514937
DOI: 10.1006/JABR.1993.1024
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description: scientific article; zbMATH DE number 168592