Analysis in matrix space and Speh's representations
type: Item
instance of: scholarly article
title: Analysis in matrix space and Speh's representations
zbMATH Open document ID: 0728.22010
DOI: 10.1007/BF01231507
author: Siddhartha Sahi
author: Elias M. Stein
published in: Inventiones Mathematicae
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143808
review text: The unitary representations of GL(n,R) are obtained, via unitary parabolic induction, from a tensor product of unitary representations which are either one-dimensional, special (``Speh'') or a complementary series representation constructed from one of these. In this paper an explicit realization of the special representations is constructed using harmonic analysis. As a consequence it is shown that every unitary representation of GL(n,R) remains irreducible upon restriction to the subgroup \(P_ n\) consisting of matrices whose last row is (0,...,0,1). This had been conjectured by A. Kirillov in 1962.
Mathematics Subject Classification ID: 22E30
Mathematics Subject Classification ID: 43A85
Mathematics Subject Classification ID: 22E45
zbMATH DE Number: 4202613
zbMATH Keywords: unitary representations of GL(n,R)
zbMATH Keywords: parabolic induction
zbMATH Keywords: tensor product
zbMATH Keywords: complementary series representation
zbMATH Keywords: special representations
reviewed by: Birgit Speh
MaRDI profile type: Publication
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OpenAlex ID: W2007143372
description: scientific article; zbMATH DE number 4202613