On the irreducibility of representations of measurable current groups
type: Item
instance of: scholarly article
title: On the irreducibility of representations of measurable current groups
zbMATH Open document ID: 0851.47047
DOI: 10.1007/BF01076495
author: R. S. Ismagilov
publication date: 1995-09-27T00:00:00Z
review text: The main result is Theorem 4 in \S 8, which presents a necessary and sufficient condition (in terms of the cocycle \(r_x\)) for the irreducibility of the representations \[ \varphi\mapsto \exp (-|r(\varphi )|^2/2) T(\pi(\varphi), r(\varphi), -r(\varphi^{-1})) \] of the measurable current group \(G^x\) [cf. for example, \textit{H. Araki}, Publ. Res. Inst. Math. Sci., Kyoto Univ. 5 (1969), 361-422 (1970; Zbl 0238.22014), or \textit{K. R. Parthasarathy} and \textit{K. Schmidt}, Acta Math. 128, 53-71 (1972; Zbl 0233.22003)].
Mathematics Subject Classification ID: 47N50
Mathematics Subject Classification ID: 81R10
Mathematics Subject Classification ID: 47A60
Mathematics Subject Classification ID: 22E45
Mathematics Subject Classification ID: 22D10
zbMATH DE Number: 795613
zbMATH Keywords: cocycle
zbMATH Keywords: irreducibility
zbMATH Keywords: representations
zbMATH Keywords: measurable current group
MaRDI profile type: Publication
cites work: Factorizable representation of current algebra. Non commutative extension of the Levy-Kinchin formula and cohomology of a solvable group with values in a Hilbert space
cites work: Factorisable representations of current groups and the Araki-Woods imbedding theorem
cites work: Irréductibilité de certaines représentations de \(G^{(x)}\)
cites work: Symmetric Hilbert spaces and related topics. Infinitely divisible positive definite functions, continuous products and tensor products, Gaussian and Poissonian stochastic processes
full work available at URL: https://doi.org/10.1007/bf01076495
OpenAlex ID: W2171829846
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 795613