Quantum Groups, Integrable Statistical Models and Knot Theory

The lectures in this volume discuss topics in statistical mechanics, the geometric and algebraic approaches to q-deformation theories, two-dimensional gravity and related problems of mathematical physics, including Vassiliev invariants and the Jones polynomials, the R-matrix with Z-symmetry, reflection equations and quantum algebra, W-geometry, braid linear algebra, holomorphic q-difference systems and q-Poincaré algebra.Contents: Lectures on Quantum Groups: Representations and Duality (V K Dobrev)Bethe Ansatz and Quantum Groups (H J de Vega)W-Geometries and Two-Dimensional Gravity (J-L Gervais)Spectral Problem in the Quantum Inverse Scattering Method.

The Goryacher-Chaplygin Top (I V Komarov)Vassiliev Invariants and the Jones Polynomials (L H Kauffman)Aspects of Yangian-Invariant Factorized S-Matrices (N J MacKay)Beyond Supersymmetry and Quantum Symmetry (S Majid)Q-Deformation of the Conformal Algebra (Z Popowicz)Infinite Dimensional R Matrix with Complete Z Symmetry (Y Shibukawa)On Representation Theories of Iwanori-Hecke Algebras Hq(W) at Roots q of Unity (H Yamane)Readership: Mathematical physicists.