Characters and fusion rules for \(W\)-algebras via quantized Drinfeld- Sokolov reduction
type: Item
instance of: scholarly article
title: Characters and fusion rules for \(W\)-algebras via quantized Drinfeld- Sokolov reduction
zbMATH Open document ID: 0768.17008
DOI: 10.1007/BF02096589
author: Minoru Wakimoto
author: Edward Frenkel
author: Victor G. Kac
published in: Communications in Mathematical Physics
publication date: 1993-01-16T00:00:00Z
review text: Realization of \(W\)-algebras \(W(\bar{\mathfrak{g}})\), associated to any simple finite-dimensional Lie algebra \(\bar{\mathfrak{g}}\), appearing as a result of quantization of the Drinfeld-Sokolov reduction, is used. This approach allows to construct a functor \(F\) from the category of positive energy representations of the affine algebra \(\mathfrak g\) to the category of positive energy representations of the algebra \(W(\bar{\mathfrak{g}})\). This functor is applied to admissible (conjecturally = all modular invariant) representations of \(\mathfrak g\) of fractional levels. The functor \(F\) is also used in evaluating characters of \(W(\bar{\mathfrak{g}})\)-modules. The calculations give many informations about conformal field theory with \(W(\bar{\mathfrak{g}})\)-symmetry. In particular, Verlinde's formula for the modular transform of \(W(\bar{\mathfrak{g}})\)-characters to describe the fusion algebra of the minimal \(W(\bar{\mathfrak{g}})\)-models is applied. Because the application of Verlinde's arguments to affine characters at a fractional level can lead to negative fusion coefficients, the use of the functor \(F\) is essential in this case.
reviewed by: A. Dzhumadil'daev
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 81R50
zbMATH DE Number: 95413
zbMATH Keywords: \(W\)-algebras
zbMATH Keywords: Drinfeld-Sokolov reduction
zbMATH Keywords: characters
zbMATH Keywords: fusion coefficients
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 95413