The behavior at infinity of the Bruhat decomposition
type: Item
instance of: scholarly article
title: The behavior at infinity of the Bruhat decomposition
zbMATH Open document ID: 0935.14029
author: Michel Brion
published in: Commentarii Mathematici Helvetici
publication date: 2000-05-10T00:00:00Z
review text: Summary: For a connected reductive group \(G\) and a Borel subgroup \(B\), we study the closures of double classes \(BgB\) in a \((G\times G)\)-equivariant ``regular'' compactification of \(G\). We show that these closures \(\overline{BgB}\) intersect properly all \((G\times G)\)-orbits, with multiplicity one, and we describe the intersections. Moreover, we show that almost all \(\overline {BgB}\) are singular in codimension two exactly. We deduce this from more general results on \(B\)-orbits in a spherical homogeneous space \(G/H\); they lead to formulas for homology classes of \(H\)-orbit closures in \(G/B\), in terms of Schubert cycles.
Mathematics Subject Classification ID: 14L30
Mathematics Subject Classification ID: 14M17
Mathematics Subject Classification ID: 14M15
zbMATH DE Number: 1146266
zbMATH Keywords: Bruhat decomposition
zbMATH Keywords: equivariant compactification
zbMATH Keywords: regular embedding
zbMATH Keywords: spherical homogeneous space
zbMATH Keywords: Schubert cycles
MaRDI profile type: Publication
full work available at URL: s000140050049
OpenAlex ID: W2024233267
DOI: 10.1007/S000140050049
description: scientific article; zbMATH DE number 1146266