Fock space representations of Virasoro algebra and intertwining operators
type: Item
instance of: scholarly article
title: Fock space representations of Virasoro algebra and intertwining operators
zbMATH Open document ID: 0611.17006
author: Yukihiro Kanie
author: Akihiro Tsuchiya
published in: Proceedings of the Japan Academy. Series A
publication date: 1986-01-01T00:00:00Z
review text: The Virasoro algebra \(L\) 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 is a central extension of the Lie algebra of polynomial vector fields on the circle. 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 left \(L\)-modules, called the Verma modules, and obtained a formula for the determinants of the matrices of their vacuum expectation values. Feigin and Fuks used the formula to determine the composition series. In this note, another kind of representations of \(L\), called the Fock space representations, and intertwining operators between them are constructed. The analogous determinant formula for them is given.
Mathematics Subject Classification ID: 17B68
Mathematics Subject Classification ID: 81R10
zbMATH DE Number: 3987519
zbMATH Keywords: Virasoro algebra
zbMATH Keywords: central extension
zbMATH Keywords: Lie algebra of polynomial vector fields
zbMATH Keywords: Verma modules
zbMATH Keywords: Fock space representations
zbMATH Keywords: intertwining operators
zbMATH Keywords: determinant formula
reviewed by: L. N. Vaserstein
MaRDI profile type: Publication
full work available at URL: pjaa.62.12
OpenAlex ID: W1969506068
cites work: Q3688825
cites work: Invariant skew-symmetric differential operators on the line and Verma modules over the Virasoro algebra
cites work: Q3041386
cites work: Q3693664
cites work: Q5845916
cites work: Fock space representations of the Virasoro algebra. Intertwining operators
DOI: 10.3792/PJAA.62.12
description: scientific article; zbMATH DE number 3987519