Kac-Moody group representations and generalization of the Sugawara construction of the Virasoro algebra
type: Item
instance of: scholarly article
title: Kac-Moody group representations and generalization of the Sugawara construction of the Virasoro algebra
zbMATH Open document ID: 0657.17014
DOI: 10.1007/BF00402018
author: Víctor Aldaya
author: José Navarro-Salas
published in: Letters in Mathematical Physics
publication date: 1988-01-01T00:00:00Z
review text: In the present paper the authors use a previously developed perturbative technique for calculating group laws. The group they apply their techniques to is the infinite-dimensional Lie group with as Lie algebra the semidirect product of the Virasoro algebra V with the affine Kac- Moody algebra of sl(2,\({\mathbb{R}})\) (i.e. the Kac-Moody algebra \(A_ 1^{(1)}).\) They give the commutation relations of \(\tilde V\times A_ 1^{(1)}\), parametrized so as to include all nontrivial central extensions. They classify all possible characteristic subalgebras, leading to different polarizations and then to different representations with a determined vacuum symmetry. The corresponding group law is given as a power series in the parameters (up to fourth order). Making use of this they can give perturbative expressions for the wave functions of representations of the group, and then of the actions of the Lie algebra generators on the wave functions. The highest weight representations considered here are associated with strings on SU(2).
Mathematics Subject Classification ID: 17B67
Mathematics Subject Classification ID: 22E65
Mathematics Subject Classification ID: 17B15
Mathematics Subject Classification ID: 17B10
Mathematics Subject Classification ID: 81T99
zbMATH DE Number: 4073236
zbMATH Keywords: Sugawara construction
zbMATH Keywords: perturbative technique
zbMATH Keywords: group laws
zbMATH Keywords: infinite- dimensional Lie group
zbMATH Keywords: Virasoro algebra
zbMATH Keywords: affine Kac-Moody algebra
zbMATH Keywords: commutation relations
zbMATH Keywords: central extensions
zbMATH Keywords: subalgebras
zbMATH Keywords: polarizations
zbMATH Keywords: vacuum symmetry
zbMATH Keywords: wave functions of representations
zbMATH Keywords: highest weight representations
zbMATH Keywords: strings
MaRDI profile type: Publication
cites work: Formal group laws for affine Kac-Moody groups and group quantization
cites work: Quantization as a consequence of the symmetry group: An approach to geometric quantization
cites work: Group manifold analysis of the structure of relativistic quantum dynamics
cites work: Current algebras and Wess-Zumino model in two dimensions
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description: scientific article; zbMATH DE number 4073236