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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.

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Author: G. Pastore
Updated : 04 Sep 2003
URL: http://www-dft.ts.infn.it/DFT/activities/pfurlan.html