Unitary quasi-finite representations of \(W_\infty\)
type: Item
instance of: scholarly article
title: Unitary quasi-finite representations of \(W_\infty\)
zbMATH Open document ID: 0974.17033
DOI: 10.1023/A:1026577132470
author: Victor G. Kac
author: Jose I. Liberati
published in: Letters in Mathematical Physics
publication date: 2001-12-13T00:00:00Z
review text: \textit{H. Awata, M. Fukuma, Y. Matsuo} and \textit{S. Odake} [J. Phys. A 28, 105-112 (1995; Zbl 0852.17025)] developed a theory of quasi-finite highest-weight representations of the subalgebras \(W_{\infty, p}\) (\(p\in\mathbb C[x]\)) of \(W_{1+\infty}\), the most important being \(W_{\infty}=W_{\infty, x}\). In the paper under review the authors develop a general approach to these problems by following the basic ideas in [\textit{V. Kac} and \textit{A. Radul}, Commun. Math. Phys. 157, 429-457 (1993; Zbl 0826.17026)]. The main result is the classification and construction of all unitary irreducible quasi-finite highest-weight modules over \(W_{\infty}\). These modules are realized in terms of unitary highest-weight representations of the Lie algebra of infinite matrices with finitely many nonzero diagonals.
Mathematics Subject Classification ID: 17B68
Mathematics Subject Classification ID: 81R10
Mathematics Subject Classification ID: 17B70
zbMATH DE Number: 1552987
zbMATH Keywords: quasi-finite highest-weight modules
reviewed by: Mirko Primc
MaRDI profile type: Publication
full work available at URL: a:1026577132470
OpenAlex ID: W107561696
description: scientific article; zbMATH DE number 1552987