Representations of pseudo-unitary groups associated with a cone
type: Item
instance of: scholarly article
title: Representations of pseudo-unitary groups associated with a cone
zbMATH Open document ID: 0941.22015
published in: Lobachevskii Journal of Mathematics
publication date: 2000-04-09T00:00:00Z
full work available at URL: https://eudml.org/doc/224151
full work available at URL: molcha.htm
review text: The representations of the pseudo-unitary group \(SU(p,q)\), \(p,q\geq 2\), associated with an isotropic cone are studied. These representations are important in constructing harmonic analysis on hyperbolic spaces. The main instrument used in this paper is the restriction to the maximal compact subgroup \(K=S(U(p) \times U(q))\). The zonal spherical functions for \(K\)-types are obtained and the structure of representations associated with a cone (irreducibility, composition series, etc.) is studied. The intertwining operators and invariant Hermitian forms are determined in order to establish which representations are unitarizable. The author concludes that the representations in the first and second discrete series, the exceptional representation and the unit representation are unitarizable.
Mathematics Subject Classification ID: 22E46
zbMATH DE Number: 1413897
zbMATH Keywords: composition series
zbMATH Keywords: sesquilinear forms
zbMATH Keywords: unitarizability
zbMATH Keywords: \(K\)-types
zbMATH Keywords: pseudounitary group
zbMATH Keywords: isotropic cone
zbMATH Keywords: representations
zbMATH Keywords: harmonic analysis
zbMATH Keywords: hyperbolic spaces
zbMATH Keywords: zonal spherical functions
zbMATH Keywords: intertwining operators
zbMATH Keywords: Hermitian forms
zbMATH Keywords: first and second discrete series
zbMATH Keywords: exceptional representation
author: V. F. Molchanov
reviewed by: Gheorghe Zet
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1413897