Quantum Groups: Proceedings of Workshops held in the Euler International Mathematical Institute, Leningrad, Fall 1990

V. G. Drinfeld (auth.), Petr P. Kulish (eds.)3540553053, 9783540553052, 0387553053

The theory of Quantum Groups is a rapidly developing area with numerous applications in mathematics and theoretical physics, e.g. in link and knot invariants in topology, q-special functions, conformal field theory, quantum integrable models. The aim of the Euler Institute’s workshops was to review and compile the progress achieved in the different subfields. Near 100 participants came from 14 countries. More than 20 contributions written up for this book contain new, unpublished material and half of them include a survey of recent results in the field (deformation theory, graded differential algebras, contraction technique, knot invariants, q-special functions). FROM THE CONTENTS: V.G. Drinfeld: On Some Unsolved Problems in Quantum Group Theory.- M. Gerstenhaber, A. Giaquinto, S.D. Schack: Quantum Symmetry.- L.I. Korogodsky,L.L. Vaksman: Quantum G-Spaces and Heisenberg Algebra.-J. Stasheff: Differential Graded Lie Algebras, Quasi-Hopf Algebras and Higher Homotopy Algebras.- A.Yu. Alekseev, L.D. Faddeev, M.A. Semenov-Tian-Shansky: Hidden Quantum Groups inside Kac-Moody Algebras.- J.-L. Gervais: Quantum Group Symmetry of 2D Gravity.- T. Kohno: Invariants of 3-Manifolds Based on Conformal Field Theory and Heegaard Splitting.- O. Viro: Moves of Triangulations of a PL-Manifold.

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Table of contents :
On some unsolved problems in quantum group theory….Pages 1-8
Quantum symmetry….Pages 9-46
Yang-Baxter equation and deformation of associative and Lie algebras….Pages 47-55
Quantum G -spaces and Heisenberg algebra….Pages 56-66
Real and imaginary forms of quantum groups….Pages 67-78
Rank of quantum groups and braided groups in dual form….Pages 79-89
Yangians of the “strange” lie superalgebras….Pages 90-97
Askey-wilson polynomials as spherical functions on SU q (2)….Pages 98-103
Twisted yangians and infinite-dimensional classical Lie algebras….Pages 104-119
Differential graded Lie algebras, quasi-hopf algebras and higher homotopy algebras….Pages 120-137
Quantum deformation of the flag variety….Pages 138-141
Zonal spherical functions on quantum symmetric spaces and MacDonald’s symmetric polynomials….Pages 142-147
Hidden quantum groups inside Kac-Moody algebras….Pages 148-158
Liouville theory on the lattice and universal exchange algebra for bloch waves….Pages 159-175
Non-local currents in 2D QFT: An alternative to the quantum inverse scattering method….Pages 176-196
Induced representations and tensor operators for quantum groups….Pages 197-209
Affine toda field theory: S-matrix vs perturbation….Pages 210-220
Contractions of quantum groups….Pages 221-244
New solutions of Yang-Baxter equations and quantum group structures….Pages 245-258
Quantum group symmetry of 2D gravity….Pages 259-276
Extended chiral conformal theories with a quantum symmetry….Pages 277-302
Fusion rsos models and rational coset models….Pages 303-311
Integrable time-discrete systems: Lattices and mappings….Pages 312-325
On relations between poisson groups and quantum groups….Pages 326-334
Characters of Hecke and Birman-Wenzl algebras….Pages 335-340
Invariants of 3-Manifolds based on conformal field theory and Heegaard splitting….Pages 341-349
The multi-variable alexander polynomial and a one—parameter family of representations of U q (sl(2,C)) at q 2 =−1….Pages 350-353
Preparation theorems for isotopy invariants of links in 3-manifolds….Pages 354-362
Quantum invariants of 3-manifold and a glimpse of shadow topology….Pages 363-366
Moves of triangulations of a PL-manifold….Pages 367-372
Yang-Baxter relation, exactly solvable models and link polynomials….Pages 373-388
Triangularity of transition matrices for generalized Hall-Littlewood polynomials….Pages 389-390
An open problem in quantum groups….Pages 391-392
Two problems in quantized algebras of functions….Pages 393-393
Unsolved problems….Pages 394-394
On classification of ℤ-graded Lie algebras of constant growth which have algebra ℂ[ h ] as Cartan subalgebra….Pages 395-395