Projective representations of the current group \(\text{SU} (1,1)^ X\)
type: Item
instance of: scholarly article
title: Projective representations of the current group \(\text{SU} (1,1)^ X\)
zbMATH Open document ID: 0832.43007
publication date: 1994-12-05T00:00:00Z
review text: Let \(G\) be the pseudo-unitary group SU(1,1) and let \(X\) be a topological space with continuous measure \(dx\). Then we can construct the group \(G^X\) of all measurable maps \(f : X \to G\) with pointwise multiplication. In a previous paper the authors constructed families of irreducible unitary representations of \(G^X\), associated to representations of the group \(G\) by motions of a real Hilbert space. In this paper, instead of representations of \(G\) by motions of a real Hilbert space, the authors consider representations of \(G\) by motions of a complex Hilbert space. There are two series of irreducible representations of \(G\) of this kind. Starting with these representations, two new series of irreducible unitary representations of the group \(G^X\) are constructed. Unlike the representations constructed by means of real Hilbert spaces, these representations are projective. They can be considered as square roots of the faithful representations constructed before. It is indicated that similar series of representations for the current group \(\text{SU} (n,1)^X\), \(n > 1\), can be constructed.
Mathematics Subject Classification ID: 43A65
Mathematics Subject Classification ID: 22E45
zbMATH DE Number: 687604
zbMATH Keywords: projective representations
zbMATH Keywords: groups of measurable maps
zbMATH Keywords: current group
zbMATH Keywords: irreducible unitary representations
author: I. M. Gel'fand
author: M. I. Graev
reviewed by: A. U. Klimyk
MaRDI profile type: Publication
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published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 687604