[ Department of Theoretical Physics ]

Quantum Groups and Infinite-dimensional Algebras

Prof. Paolo Furlan, Associate Professor

We have constructed the fusion ring of a quasi-rational {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 Kac-Moody algebra. We define the chiral zero modes' phase space of the SU(n) WZNW model. This classical system exhibits a Poisson-Lie symmetry that evolves upon quantization into an Uq(sln) symmetry. The resulting Poisson brackets appear as the classical counterpart of the exchange relations of a quantum matrix algebra studied previously.


Author: G. Pastore
Updated :
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