Isotropy irreducible spaces and \(s\)-representations
type: Item
instance of: scholarly article
title: Isotropy irreducible spaces and \(s\)-representations
zbMATH Open document ID: 0845.53036
DOI: 10.1016/0926-2245(96)89148-0
author: Wolfgang Ziller
author: Ernst Heintze
published in: Differential Geometry and its Applications
publication date: 1996-09-04T00:00:00Z
review text: A homogeneous space \(G/K\) is called isotropy irreducible if the action of the isotropy group \(K\) on its tangent space is irreducible. Classical examples are the irreducible symmetric spaces. The non-symmetric isotropy irreducible spaces with \(K\) compact and connected have been classified by O. V. Manturov and J. A. Wolf. It turns out that \(G\) is compact and simple. If \(G= \text{SO}(n)\), \(\text{SU}(n)\) or \(\text{Sp}(n)\), these spaces are again related to symmetric spaces as had been observed by C. T. C. Wall at looking at the list of Wolf. The paper gives a new and simple conceptual proof for this relation. To this end a characterization of isotropy representations of symmetric spaces is given.
Mathematics Subject Classification ID: 53C30
Mathematics Subject Classification ID: 53C35
zbMATH DE Number: 897474
zbMATH Keywords: isotropy irreducible homogeneous space
zbMATH Keywords: isotropy representations of symmetric spaces
Wikidata QID: Q115362477
MaRDI profile type: Publication
full work available at URL: 0926-2245(96)89148-0
OpenAlex ID: W2044351118
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description: scientific article; zbMATH DE number 897474