A classification of parabolic subgroups of classical groups with a finite number of orbits on the unipotent radical
type: Item
instance of: scholarly article
title: A classification of parabolic subgroups of classical groups with a finite number of orbits on the unipotent radical
zbMATH Open document ID: 0924.20035
DOI: 10.1007/BF01236661
author: Gerhard Röhrle
author: Lutz Hille
published in: Transformation Groups
publication date: 1999-11-10T00:00:00Z
review text: Let \(G\) be a classical algebraic group over an algebraically closed field. The authors classify all instances when a parabolic subgroup \(P\) of \(G\) acts on its unipotent radical \(P_u\), or on \(\mathfrak p_u\), the Lie algebra of \(P_u\), with only a finite number of orbits, and furthermore obtain a combinatorial formula for the number of orbits in the finite cases for general linear groups.
reviewed by: Chiu Sen
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 20G15
zbMATH DE Number: 1286198
zbMATH Keywords: algebraic groups
zbMATH Keywords: parabolic subgroups
zbMATH Keywords: unipotent radicals
zbMATH Keywords: numbers of orbits
zbMATH Keywords: general linear groups
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01236661
OpenAlex ID: W1964345772
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description: scientific article; zbMATH DE number 1286198