**CRM Proceedings & Lecture Notes**

Volume: 26;
2000;
264 pp;
Softcover

MSC: Primary 81; 82; 33; 35;
Secondary 37; 70

**Print ISBN: 978-0-8218-2093-3
Product Code: CRMP/26**

List Price: $102.00

AMS Member Price: $81.60

MAA Member Price: $91.80

**Electronic ISBN: 978-1-4704-3940-8
Product Code: CRMP/26.E**

List Price: $96.00

AMS Member Price: $76.80

MAA Member Price: $86.40

# Integrable Systems: From Classical to Quantum

Share this page *Edited by *
*J. Harnad; G. Sabidussi; P. Winternitz*

A co-publication of the AMS and Centre de Recherches Mathématiques

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
many-particle 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 Seiberg-Witten approach to supersymmetric
Yang-Mills 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 cross-section 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 up-to-date
introduction and an overview of many of the main areas of study in the theory
of integral systems.

Titles in this series are co-published with the Centre de Recherches Mathématiques.

#### Readership

Graduate students and research mathematicians interested in integrable systems; theoretical physicists.

# Table of Contents

## Integrable Systems: From Classical to Quantum

- Cover Cover11
- Title page iii4
- Contents v6
- Preface vii8
- Photo ix10
- Key to group picture x11
- List of participants xiii14
- Authors’ addresses xv16
- On the chiral WZNW phase space, exchange r-matrices and Poisson-Lie groupoids 118
- Loop groups, 𝑅-matrices and separation of variables 2138
- The geometry of generalised Hitchin systems 5572
- Determinant representation for form factors 7794
- Isomonodromic deformations in genus zero and one: Algebro-geometric solutions and Schlesinger transformations 87104
- Quantum inverse scattering problem and correlation functions of integrable models 105122
- Multiseparability and superintegrability for classical and quantum systems 129146
- Integrability and symmetry of the XXZ model 157174
- Characteristic systems on Poisson Lie groups and their quantization 165182
- Special functions associated with Calogero-Moser type quantum systems 189206
- Bäcklund transformations and Baster’s 𝑄-operator 227244
- Universality of the distribution functions of random matrix theory 251268
- Back Cover Back Cover1282