
Quantum Groups and Infinitedimensional Algebras
Prof. 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.
