Quantum Groups

to quantum groups.- Mathematical guide to quantum groups.- A q-boson realization of the quantum group SU q (2) and the theory of q-tensor operators.- Polynomial basis for SU(2)q and Clebsch-Gordan coefficients.- U q (sl(2)) Invariant operators and reduced polynomial identities.- Classification and characters of Uq(sl(3, C ))representations.- Extremal projectors for quantized kac-moody superalgebras and some of their applications.- Yang-Baxter algebras, integrable theories and Betre Ansatz.- Yang-Baxter algebra - Bethe Ansatz - conformal quantum field theories - quantum groups.- Classical Yang-Baxter equations and quantum integrable systems (Gaudin models).- Quantum groups as symmetries of chiral conformal algebras.- Comments on rational conformal field theory, quantum groups and tower of algebras.- Chern-Simons field theory and quantum groups.- Quantum symmetry associated with braid group statistics.- Sum rules for spins in (2 + 1)-dimensional quantum field theory.- Anomalies from the phenomenological and geometrical points of view.- KMS states, cyclic cohomology and supersymmetry.- Gauge theories based on a non-commutative geometry.- Algebras symmetries spaces.

The study of quantum groups is at present the most active topic of research in mathematical physics. Here, for the first time, experts from different schools review the various approaches so far known. The workshop addresses both students and researchers.