On the modality of parabolic subgroups of linear algebraic groups
type: Item
instance of: scholarly article
title: On the modality of parabolic subgroups of linear algebraic groups
zbMATH Open document ID: 0933.20037
author: Gerhard Röhrle
published in: Manuscripta Mathematica
publication date: 2000-01-20T00:00:00Z
review text: The author generalizes to positive characteristic the ``monotonicity'' results of \textit{V. L. Popov} and \textit{G. Röhrle} [in: Algebraic groups and Lie groups, Aust. Math. Soc. Lect. Ser. 9, 297-320 (1997; Zbl 0887.14020)]. Namely, let \(G\) be a linear algebraic group over an algebraically closed field \(k\) and \(P\) be a parabolic subgroup of \(G\). It is proved that: (1) If \(P\) is stable with respect to a semisimple automorphism \(\Theta\) of \(G\), then \(\text{mod }P^\Theta\leq\text{mod }P\) (here and further \(\text{mod }Q\) stands for the modality of \(Q\), see the above mentioned paper). (2) If \(G\) is reductive, the characteristic of \(k\) is a good prime for \(G\), and \(H\) is a closed reductive subgroup of \(G\) normalized by a maximal torus of \(P\), then \(\text{mod}(P\cap H)\leq\text{mod }P\).
Mathematics Subject Classification ID: 20G15
Mathematics Subject Classification ID: 14L35
Mathematics Subject Classification ID: 17B45
zbMATH DE Number: 1251320
zbMATH Keywords: modality
zbMATH Keywords: linear algebraic groups
zbMATH Keywords: parabolic subgroups
zbMATH Keywords: orbits
zbMATH Keywords: reductive subgroups
reviewed by: Vladimir L. Popov
MaRDI profile type: Publication
full work available at URL: s002290050121
OpenAlex ID: W2014537434
DOI: 10.1007/S002290050121
description: scientific article; zbMATH DE number 1251320