CRM Proceedings & Lecture Notes 2000; 264 pp; softcover Volume: 26 ISBN10: 0821820931 ISBN13: 9780821820933 List Price: US$91 Member Price: US$72.80 Order Code: CRMP/26
 This volume presents the papers based upon lectures given at the 1999 Séminaire de Mathémathiques Supérieurs held in Montréal. It includes contributions from many of the most active researchers in the field. This subject has been in a remarkably active state of development throughout the past three decades, resulting in new motivation for study in surprisingly different directions. Beyond the intrinsic interest in the study of integrable models of manyparticle systems, spin chains, lattice and field theory models at both the classical and the quantum level, and completely solvable models in statistical mechanics, there have been new applications in relation to a number of other fields of current interest. These fields include theoretical physics and pure mathematics, for example the SeibergWitten approach to supersymmetric YangMills theory, the spectral theory of random matrices, topological models of quantum gravity, conformal field theory, mirror symmetry, quantum cohomology, etc. This collection gives a nice crosssection of the current state of the work in the area of integrable systems which is presented by some of the leading active researchers in this field. The scope and quality of the articles in this volume make this a valuable resource for those interested in an uptodate introduction and an overview of many of the main areas of study in the theory of integral systems. Titles in this series are copublished with the Centre de Recherches Mathématiques. Readership Graduate students and research mathematicians interested in integrable systems; theoretical physicists. Table of Contents  J. Balog, L. Fehér, and L. Palla  On the chiral WZNW phase space, exchange rmatrices and PoissonLie groupoids
 J. Harnad  Loop groups, \(R\)matrices and separation of variables
 J. C. Hurtubise  The geometry of generalised Hitchin systems
 V. E. Korepin  Determinant representation for form factors
 D. A. Korotkin  Isomonodromic deformations in genus zero and one: Algebrogeometric solutions and Schlesinger transformations
 J.M. Maillet  Quantum inverse scattering problem and correlation functions of integrable models
 W. Miller, Jr.  Multiseparability and superintegrability for classical and quantum systems
 T. Miwa  Integrability and symmetry of the XXZ model
 N. Reshetikhin  Characteristic systems on Poisson Lie groups and their quantization
 S. N. M. Ruijsenaars  Special functions associated with CalogeroMoser type quantum systems
 E. K. Sklyanin  Bäcklund transformations and Baster's \(Q\)operator
 C. A. Tracy and H. Widom  Universality of the distribution functions of random matrix theory
