This volume contains the lectures given by the three speakers, M Jimbo, P P Kulish and E K Sklyanin, who are outstanding experts in their field. It is essential reading to those working in the fields of Quantum Groups, and Integrable Systems.
Part 1 Quantum group and recent developments, M. Jimbo: review of representations of Uq(G); finite dimensional representations of Uq(SL(2)); universal R-matrix; problems relating with the root of unity; crystal base theory of Kashiwara (q=0). Part 2 Recent developments on quantum inverse scattering methods, E.K. Sklyanin: R matrix; representation of transfer matrices T(u); spectrum of generating function (u); correlation functions. Part 3 Quantum group as quantum integrable system, P.P. Kulish: q-oscillator, q-special functions; q-algebra as symmetry of dynamical systems with reflection; connection with CFT and Gervai's theory.