Abstract
We study the representation of chiral vertex operators for sl( N) WZNW models in the free field formalism. Exploiting the underlying quantum group structure of the free field resolution, we reduce the problem of constructing the infinite number of components of a chiral vertex to that of finding a single vector in a finite dimensional irreducible representation of U q( sl(N)) . In particular this provides a new, purely algebraic, characterization of the fusion rules. We briefly summarize the analogous construction for finite dimensional algebras and use it as a guide. Our discussion is illustrated by explicit examples of vertices in sl(2) and sl(3) WZNW models.
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