An analytic series of irreducible representations of the free group
type: Item
instance of: scholarly article
title: An analytic series of irreducible representations of the free group
zbMATH Open document ID: 0634.22003
author: Ryszard Szwarc
publication date: 1988-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/74795
review text: Let \({\mathbb{F}}_ k\) be a free group on k generators. We construct the series of uniformly bounded representations \(\prod _ z\) of \({\mathbb{F}}_ k\) acting on the common Hilbert space, depending analytically on the complex parameter z, \(1/(2k-1)<| z| <1\), such that each representation \(\prod _ z\) is irreducible. If z is real or \(| z| =1/(\sqrt{2k-1})\) then \(\prod _ z\) is unitary; in other cases \(\prod _ z\) cannot be made unitary. For \(z\neq z'\) representations \(\prod _ z\) and \(\prod _{z'}\) are congruent modulo compact operators.
reviewed by: Ryszard Szwarc
Mathematics Subject Classification ID: 22D10
zbMATH DE Number: 4031978
zbMATH Keywords: analytic series
zbMATH Keywords: free group
zbMATH Keywords: uniformly bounded representations
zbMATH Keywords: unitary representations
zbMATH Keywords: Hilbert spaces
MaRDI profile type: Publication
OpenAlex ID: W2088428865
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DOI: 10.5802/AIF.1124
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 4031978