Representations of affine Kac-Moody algebras, bosonization and resolutions

We study boson representations of the affine Kac-Moody algebras and give an explicit description of primary fields and intertwining operators, using vertex operators. We establish the resolution of the irreducible module, consisting of boson representations, and point out the connection with Virasoro algebra. All these give new bosonization procedures for Wess-Zumino-Witten (WZW) models and mathematical backgrounds for the integral representation of correlation functions in WZW models on the plane and on the torus.