Irreducible induced representations of ICC-groups
type: Item
instance of: scholarly article
title: Irreducible induced representations of ICC-groups
zbMATH Open document ID: 0759.22011
DOI: 10.1007/BF01934311
author: Michael W. Binder
published in: Mathematische Annalen
publication date: 1993-03-03T00:00:00Z
full work available at URL: https://eudml.org/doc/164987
review text: Let \(G\) be an ICC-group, i.e. \(G\) is discrete and the regular representation \(\lambda\) is a factor representation; and let \(H\) be an abelian subgroup. We study the direct integral decomposition \(\lambda=\int^ \oplus_{\widehat H}\text{ind}^ G_ H\sigma d\mu(\sigma)\) in order to find representations that are induced from finite-dimensional ones and that are irreducible as well as weakly equivalent to \(\lambda\). One section is devoted to the infinite symmetric group, where non-abelian subgroups are needed to obtain those representations. Moreover an example of a maximal abelian direct integral decomposition of a factor representation into reducible fibres is given.
Mathematics Subject Classification ID: 22D30
Mathematics Subject Classification ID: 22D20
Mathematics Subject Classification ID: 20C32
zbMATH DE Number: 126354
zbMATH Keywords: discrete group
zbMATH Keywords: induced representation
zbMATH Keywords: irreducible representations
zbMATH Keywords: ICC- group
zbMATH Keywords: regular representation
zbMATH Keywords: direct integral decomposition
zbMATH Keywords: weakly equivalent
zbMATH Keywords: infinite symmetric group
MaRDI profile type: Publication
cites work: Q3854185
cites work: Induced Representations of Discrete Groups
cites work: Sur les $C^*$-algèbres
cites work: Weak Containment and Induced Representations of Groups
cites work: Q5562332
cites work: Ein maximales Mass, dessen Träger keine Extremalpunkte enthält
cites work: Q5723435
cites work: Q3312425
cites work: The Structure of Certain Unitary Representations of Infinite Symmetric Groups
cites work: On Induced Representations of Groups
cites work: Q3940323
cites work: Certain Unitary Representations of the Infinite Symmetric Group, I
cites work: Some remarks on induced representations of infinite discrete groups
cites work: Q3963253
cites work: Q3876492
cites work: The Tomita Decomposition of Rings of Operators
cites work: Direct Integrals of Hilbert Spaces I.
description: scientific article; zbMATH DE number 126354