Conformal theories, grassmannians and soliton hierarchies. Pt. 1

We formulate conformal field theories on the infinite-dimensional grassmannian manifold. Besides recovering the known results for the central charge and correlation functions of the b-c system this formalism immediately lends itself to further generalization. The grassmannian manifold is in fact an ad hoc model for the geometrical interpretation of the irreducible representations of an infinite-dimensional Kac-Moody algebra which, in turn, admit an intertwining action of a Virasoro algebra. We further give a proof of bosonization from a purely grassmannian point of view. (orig.)