On the unitary dual of real reductive Lie groups and the \(A_g(\lambda)\) modules: The strongly regular case
type: Item
instance of: scholarly article
title: On the unitary dual of real reductive Lie groups and the \(A_g(\lambda)\) modules: The strongly regular case
zbMATH Open document ID: 0941.22014
DOI: 10.1215/S0012-7094-99-09616-3
author: Susana A. Salamanca-Riba
published in: Duke Mathematical Journal
publication date: 2000-03-27T00:00:00Z
review text: Let \(G\) be a semisimple Lie group which is connected and has finite center. Let \(\pi\) be an irreducible unitary representation whose infinitesimal character is strongly regular and real. D. Vogan and G. Zuckerman conjectured in the course of the (unsolved) classification problem of the unitary dual of \(G\) that \(\pi\) must be isomorphic to a Zuckerman module derived from a one dimensional unitary character of a Levi subgroup. This conjecture is proved in the present paper. The method goes back to ideas of D. Vogan and the author who proposed a strategy for solving the classification problem by reducing it to groups of lower dimension.
Mathematics Subject Classification ID: 22E46
Mathematics Subject Classification ID: 22D10
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 22E47
zbMATH DE Number: 1425186
zbMATH Keywords: semisimple Lie group
zbMATH Keywords: irreducible unitary representation
zbMATH Keywords: infinitesimal character
zbMATH Keywords: Zuckerman module
Wikidata QID: Q115240130
reviewed by: Anton Deitmar
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1425186