A classification of simple weakly spherical homogeneous spaces. I
type: Item
instance of: scholarly article
title: A classification of simple weakly spherical homogeneous spaces. I
zbMATH Open document ID: 0857.20026
author: Tatsuo Kimura
author: Shin-ichi Kasai
author: Shin-Ichi Otani
published in: Journal of Algebra
publication date: 1997-01-20T00:00:00Z
review text: The homogeneous space \(H\setminus G\), defined by a connected linear algebraic group \(G\) (on the field of complex numbers) and a closed subgroup \(H\), is said to be weakly spherical if it admits a Zariski dense \(P\)-orbit, where \(P\) is some parabolic subgroup of \(G\). The authors undertake the task of classifying all such homogeneous spaces for \(G=\text{GL}_n\). This is done here under some additional assumptions, yielding an explicit list of 74 cases.
Mathematics Subject Classification ID: 20G20
Mathematics Subject Classification ID: 14M17
Mathematics Subject Classification ID: 32M15
Mathematics Subject Classification ID: 14L30
zbMATH DE Number: 917733
zbMATH Keywords: connected linear algebraic groups
zbMATH Keywords: Zariski dense orbits
zbMATH Keywords: parabolic subgroups
zbMATH Keywords: homogeneous spaces
reviewed by: François Rouvière
MaRDI profile type: Publication
full work available at URL: jabr.1996.0169
OpenAlex ID: W2067257213
DOI: 10.1006/JABR.1996.0169
description: scientific article; zbMATH DE number 917733