The unitary dual of the universal covering group of \(\mathrm{GL}(n,\mathbb{R})\)
type: Item
instance of: scholarly article
title: The unitary dual of the universal covering group of \(\mathrm{GL}(n,\mathbb{R})\)
zbMATH Open document ID: 0732.22010
DOI: 10.1215/S0012-7094-90-06126-5
author: Jing-Song Huang
published in: Duke Mathematical Journal
publication date: 1990-01-01T00:00:00Z
review text: The author classifies the irreducible unitary representations of the double cover \(G\) of \(\mathrm{GL}(n,\mathbb{R})\) which do not factor to \(\mathrm{GL}(n,\mathbb{R})\) itself. The methods and techniques are similar to \textit{D. Vogan}'s in his classification of the unitary dual of \(\mathrm{GL}(n,\mathbb{R})\) [Invent. Math. 83, 449--505 (1986; Zbl 0598.22008)]. One finds that just one new building block appears in the unitary dual of \(G\). This is a unipotent representation whose Langlands parameters are obtained from those of a well-known unitary representation of \(\mathrm{GL}(n,\mathbb{R})\) by dividing by two. All unitary representations are then obtained from one of the building blocks by unitary induction and Stein complementary series.
Mathematics Subject Classification ID: 22E46
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 22D10
zbMATH DE Number: 4210437
zbMATH Keywords: general linear group
zbMATH Keywords: tensor product
zbMATH Keywords: irreducible unitary representations
zbMATH Keywords: double cover
zbMATH Keywords: unitary dual
zbMATH Keywords: Langlands parameters
zbMATH Keywords: unitary induction
zbMATH Keywords: Stein complementary series
reviewed by: William M. McGovern
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4210437