On homogeneous spaces of rank one
type: Item
instance of: scholarly article
title: On homogeneous spaces of rank one
zbMATH Open document ID: 0838.53041
DOI: 10.1016/0019-3577(95)93199-K
author: Dmitri I. Panyushev
published in: Indagationes Mathematicae. New Series
publication date: 1996-06-04T00:00:00Z
review text: A classification of homogeneous spaces of rank one is obtained. It is proved that they are either spherical or are induced from \(SL_2\) via a parabolic subgroup. A necessary and sufficient condition is given for a homogeneous space to have rank one. The author makes use of techniques developed by Vinberg, Popov, Luna a.o. A key step is the author's results on complexity and nilpotent orbits [Manuscr. Math. 83, No. 3-4, 223-237 (1994; Zbl 0822.14024)]. He also obtains an embedding characterization of homogeneous spaces of rank one.
Mathematics Subject Classification ID: 53C30
Mathematics Subject Classification ID: 14M17
zbMATH DE Number: 828210
zbMATH Keywords: rank one homogeneous spaces
zbMATH Keywords: embedding of homogeneous spaces
zbMATH Keywords: classification
reviewed by: Doru Ştefănescu
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 828210