Compression semigroups on open orbits on real flag manifolds
type: Item
instance of: scholarly article
title: Compression semigroups on open orbits on real flag manifolds
zbMATH Open document ID: 0824.22007
DOI: 10.1007/BF01293670
published in: Monatshefte für Mathematik
publication date: 1995-11-09T00:00:00Z
full work available at URL: https://eudml.org/doc/178680
review text: Let \((G,H)\) be an irreducible semisimple symmetric pair, \(P \subset G\) a parabolic subgroup. Suppose that the \(L\)-orbit of the base point in the flag manifold \(G/P\) is open. The semigroup \(S(L,P) = \{g \in G : gLP \subset LP\}\) is called the compression semigroup. The authors show that if \(P\) is minimal and \(S(L,P) = G\), then \((G,H)\) is Riemannian and give a geometric characterization of those cases where \(S(L,P)\) has non-empty interior different from \(G\). If \(G/H\) is a symmetric space of regular type, it is shown under certain additional assumptions that \(S(L,Q)\), where \(Q\) is some parabolic subgroup, is an Ol'shanskij semigroup.
Mathematics Subject Classification ID: 22A15
Mathematics Subject Classification ID: 22E15
Mathematics Subject Classification ID: 22E46
Mathematics Subject Classification ID: 20M20
Mathematics Subject Classification ID: 53C35
Mathematics Subject Classification ID: 43A85
zbMATH DE Number: 742701
zbMATH Keywords: irreducible semisimple symmetric pair
zbMATH Keywords: parabolic subgroup
zbMATH Keywords: flag manifold
zbMATH Keywords: compression semigroup
zbMATH Keywords: symmetric space
zbMATH Keywords: Ol'shanskij semigroup
author: Joachim Hilgert
author: Karl-Hermann Neeb
reviewed by: A. K. Guts
MaRDI profile type: Publication
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OpenAlex ID: W2072630326
description: scientific article; zbMATH DE number 742701