Quantum Groups and Infinitedimensional AlgebrasProf. Paolo Furlan, Associate Professor We have constructed the fusion ring of a quasirational {sl}^(4)_{k} WZNW theory at generic irrational level k. It is generated by commutative elements in the group ring Z[W] of the extended affine Weyl group W^ of the corresponding KacMoody algebra. We define the chiral zero modes' phase space of the SU(n) WZNW model. This classical system exhibits a PoissonLie symmetry that evolves upon quantization into an U_{q}(sl_{n}) symmetry. The resulting Poisson brackets appear as the classical counterpart of the exchange relations of a quantum matrix algebra studied previously. 


