Intertwining operators and unitary representations. I
type: Item
instance of: scholarly article
title: Intertwining operators and unitary representations. I
zbMATH Open document ID: 0683.22010
DOI: 10.1016/0022-1236(89)90096-7
author: Anthony W. Knapp
author: Velleda Baldoni
published in: Journal of Functional Analysis
publication date: 1989-01-01T00:00:00Z
review text: The problem of classifying the irreducible unitary representations of a semisimple Lie group G comes down to finding out whether some intertwining operators are semidefinite. In their preceding five works the authors have introduced some formulas to solve the latter problem and have used them for classifying UIR's in certain cases: SU(N,2), some other groups of real rank two, Langlands quotients obtained from maximal parabolic subgroups. But in these works there were no proofs of the formulas. In the paper reviewed the authors give the derivations of these formulas - when G has a compact Cartan subgroup.
Mathematics Subject Classification ID: 22E46
Mathematics Subject Classification ID: 22D10
zbMATH DE Number: 4118627
zbMATH Keywords: irreducible unitary representations
zbMATH Keywords: semisimple Lie group
zbMATH Keywords: intertwining operators
zbMATH Keywords: compact Cartan subgroup
reviewed by: V. F. Molchanov
MaRDI profile type: Publication
full work available at URL: 0022-1236(89)90096-7
OpenAlex ID: W1992485067
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description: scientific article; zbMATH DE number 4118627