Representation theory of a W-algebra from generalised DS reduction
P. Bowcock
Abstract
We investigate the W-algebra resulting from Drinfel'd-Sokolov reduction of a B2 WZW model with respect to the grading induced by a short root. The quantum algebra, which is generated by three fields of spin-2 and a field of spin-1, is explicitly constructed. A `free field' realisation of the algebra in terms of the zero-grade currents is given, and it is shown that these commute with a screening charge. We investigate the representation theory of the algebra using a combination of the explicit fusion method of Bauer et al. and free field methods. We discuss the fusion rules of degenerate primary fields, and give various character formulae and a Kac determinant formula for the algebra
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