Fock space representations of the Virasoro algebra. Intertwining operators
type: Item
instance of: scholarly article
title: Fock space representations of the Virasoro algebra. Intertwining operators
zbMATH Open document ID: 0604.17008
author: Akihiro Tsuchiya
author: Yukihiro Kanie
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1986-01-01T00:00:00Z
review text: The Virasoro algebra \({\mathcal L}\) is the Lie algebra over the complex numbers with generators \(e'_ 0\), \(e_ n\) (where \(n\) ranges over the integers) and the relations \(e'_ 0\) commutes with everything, \([e_ n,e_ m]=(m-n)e_{n+m}+\delta_{n+m}((m^ 3-m)/12)e'_ 0.\) It appears in string models of elementary particle physics. Quite recently it was used to analyze the critical phenomena in the two dimensional statistical physics. Kac studied the left \({\mathcal L}\)-module \(M(h,c)\) parametrized by two complex numbers h and c, called Verma module. In this paper, another kind of representations \({\mathcal F}(w,\lambda)\) of \({\mathcal L}\) parametrized by two complex numbers \(w\) and \(\lambda\) and intertwining operators between them are constructed. They are called the Fock space representations. The \({\mathcal L}\)-modules \({\mathcal F}(w,\lambda)\) and \(M(h,c)\) and their relationship are investigated.
Mathematics Subject Classification ID: 17B68
Mathematics Subject Classification ID: 81R10
zbMATH DE Number: 3975167
zbMATH Keywords: Virasoro algebra
zbMATH Keywords: intertwining operators
zbMATH Keywords: Fock space representations
reviewed by: L. N. Vaserstein
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195178069
OpenAlex ID: W2088636650
DOI: 10.2977/PRIMS/1195178069
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description: scientific article; zbMATH DE number 3975167