Finite, tame, and wild actions of parabolic subgroups in \(\text{GL}(V)\) on certain unipotent subgroups
type: Item
instance of: scholarly article
title: Finite, tame, and wild actions of parabolic subgroups in \(\text{GL}(V)\) on certain unipotent subgroups
zbMATH Open document ID: 0968.20023
author: Thomas Brüstle
author: Lutz Hille
published in: Journal of Algebra
publication date: 2001-06-07T00:00:00Z
review text: A parabolic subgroup of \(\text{GL}(V)\) is the stabilizer of a (possibly incomplete) flag of subspaces of \(V\). If \(P\) is such a parabolic subgroup, the authors study the action of \(P\) on the Lie algebra of its unipotent radical and more generally on the \(l\)-th term of the descending central series. They characterize the cases where this action has a finite number of orbits. The proof relies on seeing the orbits as isomorphism classes of some category, which is then shown to be equivalent to a category of modules over an algebra.
reviewed by: Martin Andler
Mathematics Subject Classification ID: 20G05
zbMATH DE Number: 1441812
zbMATH Keywords: group actions
zbMATH Keywords: parabolic subgroups
zbMATH Keywords: numbers of orbits
zbMATH Keywords: Lie algebras
MaRDI profile type: Publication
full work available at URL: jabr.1999.8180
OpenAlex ID: W2068110095
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DOI: 10.1006/JABR.1999.8180
description: scientific article; zbMATH DE number 1441812