One of the surveys gives a thorough analysis of a family of quantum integrable systems (Toda lattices) using the machinery of representation theory. Readers will find all the new differential geometric and Lie-algebraic methods which are currently used in the theory of integrable systems in this book. It will be indispensable to graduate students and researchers in mathematics and theoretical physics.

This book is another volume in the successful subseries "Dynamical Systems" of the Encyclopaedia of Mathematical Sciences. It focuses on new developments in the field of integrable systems and it provides a unique and comprehensive survey on new differential geometric and Lie-algebraic methods. Since other literature on these topics is often rather unreadable, this volume will be an indispensable guide to the current research which no mathematician or theoretical physicist who is interested in this field can do without.

Inhalt
Contents: Nonholonomic Dynamical Systems, Geometry of Distributions and Variational Problems by A.M. Vershik, V.Ya. Gershkovich.- Integrable Systems and Infinite Dimensional Lie Algebras by M.A. Olshanetsky, M.A. Perelomov.- Group-Theoretical Methods in the Theory of Finite-Dimensional Integrable Systems by A.G. Reyman, M.A. Semenov-Tian-Shansky.- Quantization of Open Toda Lattices by M.A. Semenov-Tian-Shansky.- Geometric and Algebraic Mechanisms of the Integrability of Hamiltonian Systems on Homogeneous Spaces and Lie Algebras by V.V. Trofimov, A.T. Fomenko.