American Mathematical Society TranslationsSeries 2 Advances in the Mathematical Sciences 2000; 321 pp; hardcover Volume: 201 ISBN10: 0821821334 ISBN13: 9780821821336 List Price: US$130 Member Price: US$104 Order Code: TRANS2/201
 Professor L. D. Faddeev's seminar at Steklov Mathematical Institute (St. Petersburg, Russia) has a record of more than 30 years of intensive work which has helped to shape modern mathematical physics. This collection, honoring Professor Faddeev's 65th anniversary, has been prepared by his students and colleagues. Topics covered in the volume include classical and quantum integrable systems (both analytic and algebraic aspects), quantum groups and generalizations, quantum field theory, and deformation quantization. Included is a history of the seminar highlighting important developments, such as the invention of the quantum inverse scattering method and of quantum groups. The book will serve nicely as a comprehensive, uptodate resource on the topic. Readership Graduate students and research mathematicians and mathematical physicists interested in integrable systems, quantum groups and string theory; theoretical physicists. Table of Contents  M. SemenovTianShansky  Some personal historic notes on our seminar
 E. Meinrenken and A. Alekseev  An elementary derivation of certain classical dynamical \(r\)matrices
 I. Ya. Aref'eva and O. A. Rytchkov  Incidence matrix description of intersection \(p\)brane solutions
 A. I. Bobenko and Yu. B. Suris  A discrete time Lagrange top and discrete elastic curves
 A. M. Budylin and V. S. Buslaev  The GelfandLevitanMarchenko equation and the longtime asymptotics of the solutions of the nonlinear Schrödinger equation
 R. M. Kashaev and A. Yu. Volkov  From the tetrahedron equation to universal \(R\)matrices
 A. N. Kirillov  On some quadratic algebras
 V. Korepin and N. Slavnov  Quantum inverse scattering method and correlation functions
 A. Losev, N. Nekrasov, and S. Shatashvili  Testing SeibergWitten solution
 J. M. Maillet and J. S. de Santos  Drinfeld twists and algebraic Bethe Ansatz
 V. B. Matveev  Darboux transformations, covariance theorems and integrable systems
 A. L. Pirozerski and M. A. SemenovTianShansky  Generalized \(q\)deformed GelfandDickey structures on the group of \(q\)pseudodifference operators
 A. K. Pogrebkov  On time evolutions associated with the nonstationary Schrödinger equation
 N. Reshetikhin and L. A. Takhtajan  Deformation quantization of Kähler manifolds
 E. K. Sklyanin  Canonicity of Bäcklund transformation: \(r\)matrix approach. I
 F. A. Smirnov  Quasiclassical study of form factors in finite volume
 V. Tarasov  Completeness of the hypergeometric solutions of the \(qKZ\) equation at level zero
