REPRESENTATION-THEORY OF LATTICE CURRENT-ALGEBRAS

Lattice current algebras were introduced as a regularization of the le ft-and right moving degrees of freedom in the WZNW model. They provide examples of lattice theories with a local quantum symmetry U-q(G). Th eir representation theory is studied in detail. In particular, we cons truct all irreducible representations along with a lattice analogue of the fusion product for representations of the lattice current algebra . It is shown that for an arbitrary number of lattice sites, the repre sentation categories of the lattice current algebras agree with their continuum counterparts.