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.

arXiv comment60 pages, harvmac.tex, 6 Postscript figures

References in corpus (5)

• Correlation Functions of the XXZ model for $\Delta <-1$
• Vertex operators in solvable lattice models
• Free Boson Representation of $q$-Vertex Operators and their Correlation Functions
• Deformation of the Wakimoto construction
• Free Field Representation for the Classical Limit of Quantum Affine Algebra

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• The algebra of q-pseudodifferential symbols and the q-W_{KP}^n algebra
• Form-factors of exponential fields in the affine A^{(1)}_{N-1} Toda model
• The deformed Virasoro algebra at roots of unity
• Lukyanov's Screening Operators for the Deformed Virasoro Algebra
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• A Collection of Exercises in Two-Dimensional Physics, Part 1
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