Parabolic subgroups of positive modality
type: Item
instance of: scholarly article
title: Parabolic subgroups of positive modality
zbMATH Open document ID: 0853.20031
DOI: 10.1007/BF00160621
author: Gerhard Röhrle
published in: Geometriae Dedicata
publication date: 1997-01-06T00:00:00Z
review text: The author proves a criterion for a parabolic subgroup \(P\) of a reductive algebraic group \(G\) to be of positive modality. This condition is simply a lower bound on the length of the descending central series of the radical. He also shows that in this situation we can always find a proper \(P\)-invariant linear subspace in the Lie algebra of the radical of \(P\) which admits an infinite number of \(P\)-orbits, unless \(P\) is maximal.
Mathematics Subject Classification ID: 20G20
Mathematics Subject Classification ID: 22E20
Mathematics Subject Classification ID: 20F14
Mathematics Subject Classification ID: 17B45
zbMATH DE Number: 874091
zbMATH Keywords: parabolic subgroups
zbMATH Keywords: reductive algebraic groups
zbMATH Keywords: positive modality
zbMATH Keywords: descending central series
zbMATH Keywords: radicals
zbMATH Keywords: Lie algebras
reviewed by: Chiu Sen
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00160621
OpenAlex ID: W1995284882
description: scientific article; zbMATH DE number 874091