Lecture Notes in Mathematics

On some unsolved problems in quantum group theory.- Quantum symmetry.- Yang-Baxter equation and deformation of associative and Lie algebras.- Quantum G-spaces and Heisenberg algebra.- Real and imaginary forms of quantum groups.- Rank of quantum groups and braided groups in dual form.- Yangians of the "strange" lie superalgebras.- Askey-wilson polynomials as spherical functions on SU q(2).- Twisted yangians and infinite-dimensional classical Lie algebras.- Differential graded Lie algebras, quasi-hopf algebras and higher homotopy algebras.- Quantum deformation of the flag variety.- Zonal spherical functions on quantum symmetric spaces and MacDonald's symmetric polynomials.- Hidden quantum groups inside Kac-Moody algebras.- Liouville theory on the lattice and universal exchange algebra for bloch waves.- Non-local currents in 2D QFT: An alternative to the quantum inverse scattering method.- Induced representations and tensor operators for quantum groups.- Affine toda field theory: S-matrix vs perturbation.- Contractions of quantum groups.- New solutions of Yang-Baxter equations and quantum group structures.- Quantum group symmetry of 2D gravity.- Extended chiral conformal theories with a quantum symmetry.- Fusion rsos models and rational coset models.- Integrable time-discrete systems: Lattices and mappings.- On relations between poisson groups and quantum groups.- Characters of Hecke and Birman-Wenzl algebras.- Invariants of 3-Manifolds based on conformal field theory and Heegaard splitting.- The multi-variable alexander polynomial and a one-parameter family of representations of U q (sl(2,C)) at q 2=?1.- Preparation theorems for isotopy invariants of links in 3-manifolds.- Quantum invariants of 3-manifold and a glimpse of shadow topology.- Moves of triangulations of a PL-manifold.- Yang-Baxter relation, exactly solvable models and link polynomials.- Triangularity of transition matrices for generalized Hall-Littlewood polynomials.- An open problem in quantum groups.- Two problems in quantized algebras of functions.- Unsolved problems.- On classification of ?-graded Lie algebras of constant growth which have algebra ?[h] as Cartan subalgebra.