Intertwining operators for vertex representations of toroidal Lie algebras
type: Item
instance of: scholarly article
title: Intertwining operators for vertex representations of toroidal Lie algebras
zbMATH Open document ID: 0956.17018
DOI: 10.1023/A:1007401215494
author: Kai Hing Lum
author: Victor Tan
published in: Letters in Mathematical Physics
publication date: 2001-03-13T00:00:00Z
review text: A toroidal Lie algebra \(\tau_{[n]}\) is the universal central extension of the Lie algebra \({\mathbf g} \otimes {\mathbb C} [ t_1 ^{\pm}, \cdots, t_n ^{\pm}]\), where \(\mathbf g\) is the finite dimensional simple Lie algebra over \({\mathbb C}\). When \(n=1\), \(\tau_{[1]}\) is an affine Lie algebra. In [\textit{S. Eswara Rao} and \textit{R. V. Moody}, Commun. Math. Phys. 159, 239-264 (1994; Zbl 0808.17018)] a vertex operator representation of \(\tau_{[n]}\) was constructed. In the paper under review the authors construct intertwining operators for the vertex representations of \(\tau_{[n]}\) and investigate how the intertwining operators depend on the way of labelling the points in the dual \({\mathbb Z} ^{n}\) of the torus \(T^{n}\).
reviewed by: Dražen Adamović
Mathematics Subject Classification ID: 17B69
Mathematics Subject Classification ID: 17B10
Mathematics Subject Classification ID: 17B67
zbMATH DE Number: 1202533
zbMATH Keywords: automorphism
zbMATH Keywords: circle action
zbMATH Keywords: toroidal Lie algebra
zbMATH Keywords: intertwining operators
zbMATH Keywords: vertex representations
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1202533