\((\mathrm{GL}(n+1,\mathbb R),\mathrm{GL}(n,\mathbb R))\) is a generalized Gelfand pair
type: Item
instance of: scholarly article
title: \((\mathrm{GL}(n+1,\mathbb R),\mathrm{GL}(n,\mathbb R))\) is a generalized Gelfand pair
zbMATH Open document ID: 1181.43005
DOI: 10.1134/S1061920808040122
published in: Russian Journal of Mathematical Physics
publication date: 2009-11-10T00:00:00Z
review text: Let \(G\) be a Lie group, and \(H\) a closed subgroup. The pair \((G,H)\) is said to be a generalized Gelfand pair if every \(G\)-invariant Hilbert subspace of \({\mathcal D}'(G/H)\), the space of distributions on the homogeneous space \(G/H\), decomposes multiplicity free. It is known that the symmetric pair \((\text{GL}(n+1,\mathbb R), \text{GL}(1,\mathbb R)\times \text{GL}(n,\mathbb R))\) is a generalized Gelfand pair. In this note it is shown that \((\text{GL}(n+1,\mathbb R), \text{GL}(n,\mathbb R))\) is a generalized Gelfand pair as well.
reviewed by: Jacques Faraut
Mathematics Subject Classification ID: 43A85
zbMATH DE Number: 5628051
zbMATH Keywords: Gelfand pair
author: Gerrit van Dijk
MaRDI profile type: Publication
cites work: (GLn+1(F), GLn(F)) is a Gelfand pair for any local field F
cites work: A new class of Gelfand pairs
cites work: Distributions spheriques sur les espaces hyperboliques
cites work: Spherical distributions on the pseudo-Riemannian space SL(n, \({\mathbb{R}})/GL(n-1,\,{\mathbb{R}})\)
cites work: Q4094928
cites work: On a class of generalized Gelfand pairs
cites work: Q3723078
full work available at URL: s1061920808040122
OpenAlex ID: W2018049604
description: scientific article; zbMATH DE number 5628051