Quantum Groups: Proceedings Of The 8th International Workshop On Mathematical Physics, Held At The Arnold Sommerfeld Institute, Clausthal, Frg, On 19-26 July 1989 (lecture Notes In Physics)

A Thorough Analysis Of Exactly Soluble Models In Nonlinear Classical Systems And In Quantum Systems As Well As Recent Studies In Conformal Quantum Field Theory Have Revealed The Structure Of Quantum Groups To Be An Interesting And Rich Framework For Mathematical And Physical Problems. In This Book, For The First Time, Authors From Different Schools Review In An Intelligible Way The Various Competing Approaches: Inverse Scattering Methods, 2-dimensional Statistical Models, Yang-baxter Algebras, The Bethe Ansatz, Conformal Quantum Field Theory, Representations, Braid Group Statistics, Noncommutative Geometry, And Harmonic Analysis. H.-d. Doebner, J.-d. Henning (eds.). Includes Bibliographical References. Introduction to quantum groups....Pages 3-28 Mathematical guide to quantum groups....Pages 29-63 A q-boson realization of the quantum group SU q (2) and the theory of q-tensor operators....Pages 67-88 Polynomial basis for SU (2) q and Clebsch-Gordan coefficients....Pages 89-95 U q ( sl (2)) Invariant operators and reduced polynomial identities....Pages 96-106 Classification and characters of U q (sl(3, C ))representations....Pages 107-117 Extremal projectors for quantized kac-moody superalgebras and some of their applications....Pages 118-125 Yang-Baxter algebras, integrable theories and Betre Ansatz....Pages 129-182 Yang-Baxter algebra — Bethe Ansatz — conformal quantum field theories — quantum groups....Pages 183-218 Classical Yang-Baxter equations and quantum integrable systems (Gaudin models)....Pages 219-227 Quantum groups as symmetries of chiral conformal algebras....Pages 231-277 Comments on rational conformal field theory, quantum groups and tower of algebras....Pages 278-306 Chern-Simons field theory and quantum groups....Pages 307-317 Quantum symmetry associated with braid group statistics....Pages 318-339 Sum rules for spins in (2 + 1)-dimensional quantum field theory....Pages 340-348 Anomalies from the phenomenological and geometrical points of view....Pages 349-371 KMS states, cyclic cohomology and supersymmetry....Pages 375-397 Gauge theories based on a non-commutative geometry....Pages 398-425 Algebras symmetries spaces....Pages 426-434 Recent studies in conformal quantum field theory have revealed the structure of quantum groups to be a viable framework for mathematical and physical problems. This volume explores various approaches including inverse scattering methods, non-commutative geometry and harmonic analysis.