Representations of affine Kac-Moody algebras, bosonization and resolutions
The Fock space over the infinite Heisenberg algebra can be made into a two-parameter module over the Virasoro algebra. This family of two- parameter modules contains certain submodules, chains, which from a physical point of view are primary fields while the intertwining operators yield the screening operators. These operators allow one to construct a representation of correlation functions of some 2-dimensional statistical models (on the plane and torus). The authors study boson representations of affine Kac-Moody algebras -- certain highest weight modules called Wakimoto modules and with their help they explicitly describe primary fields and, using vertex operators, the intertwining operators. A resolution of an irreducible Wakimoto module similar to the BGG-resolution is given and certain semi-infinite cohomologies of the nilpotent subalgebra (of the considered Kac-Moody algebra) are calculated. All these give new procedures for bosonization of Wess-Zumino-Witten models and the integral representation of correlation functions in WZW models on the plane and the torus.
integral representation of correlation functions
scientific article; zbMATH DE number 4168906