On a class of generalized Gelfand pairs
type: Item
instance of: scholarly article
title: On a class of generalized Gelfand pairs
zbMATH Open document ID: 0613.43009
DOI: 10.1007/BF01160476
published in: Mathematische Zeitschrift
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173806
review text: Let G/H be a pseudo-Riemannian symmetric space of rank one. The author limits himself to the groups G which are the connected Lie subgroups of the simply connected complex Lie groups \(G_ c\) (the Lie algebra of \(G_ c\) is the complexification of the Lie algebra of G). The main result of the reviewed article is that all such pairs (G,H) are generalized Gelfand pairs (i.e. each continuous unitary representation of G which can be realized on G/H is multiplicity-free) except the pairs \((Spin(1,q+1)\), Spin(1,q)), \(q\geq 1\).
Mathematics Subject Classification ID: 43A85
Mathematics Subject Classification ID: 53C35
zbMATH DE Number: 3992130
zbMATH Keywords: pseudo-Riemannian symmetric space
zbMATH Keywords: generalized Gelfand pairs
author: Gerrit van Dijk
reviewed by: V. F. Molchanov
MaRDI profile type: Publication
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OpenAlex ID: W1985235811
description: scientific article; zbMATH DE number 3992130