The Bruhat order on symmetric varieties
type: Item
instance of: scholarly article
title: The Bruhat order on symmetric varieties
zbMATH Open document ID: 0704.20039
DOI: 10.1007/BF00147354
author: Tonny A. Springer
author: R. W. jun. Richardson
published in: Geometriae Dedicata
publication date: 1990-01-01T00:00:00Z
review text: Let G be a connected reductive linear algebraic group over an algebraically closed field of characteristic \(\neq 2\). Let \(\theta\) be an automorphism of G of order 2. Let K be the fixed point subgroup of \(\theta\). Then \(X(=G/K)\) is called the symmetric variety defined by (G,\(\theta\)). Let B be a \(\theta\)-stable Borel subgroup of G. It is known that the number of double cosets BgK is finite. We have a natural partial order on the set of B-orbits in X (for the action of B on X by left translations), namely, given two B-orbits O, \(O'\), we define \(O'\leq O\), if \(O'\) is contained in the Zariski closure of O. (The authors refer to this partial order as the Bruhat order on the symmetric variety X.) In this paper, the authors give a combinatorial description of the Bruhat order on the symmetric variety X.
Mathematics Subject Classification ID: 20G15
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 14L30
zbMATH DE Number: 4154733
zbMATH Keywords: connected reductive linear algebraic group
zbMATH Keywords: automorphism
zbMATH Keywords: symmetric variety
zbMATH Keywords: Borel subgroup
zbMATH Keywords: double cosets
zbMATH Keywords: B-orbits
zbMATH Keywords: action
zbMATH Keywords: Zariski closure
zbMATH Keywords: Bruhat order
reviewed by: V. Lakshmibai
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00147354
OpenAlex ID: W2006130337
description: scientific article; zbMATH DE number 4154733