Bosonization of ZF Algebras: Direction Toward Deformed Virasoro Algebra

Abstract

These lectures were prepared to be presented at A.A. Belavin seminar on CFT at Landau Institute for Theoretical Physics. We review bosonization of CFT and show how it can be applied to the studying of representations of Zamolodchikov-Faddeev (ZF) algebras. In the bosonic construction we obtain explicit realization of chiral vertex operators interpolating between irreducible representations of the deformed Virasoro algebra. The commutation relations of these operators are determined by the elliptic matrix of IRF type and their matrix elements are given in the form of the contour integrals of some meromorphic functions.