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Advances in the Mathematical Sciences
Moscow Seminar in Mathematical Physics
Edited by: A. Yu. Morozov and M. A. Olshanetsky, Institute of Theoretical and Experimental Physics, Moscow, Russia
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American Mathematical Society Translations--Series 2
Advances in the Mathematical Sciences
1999; 299 pp; hardcover
Volume: 191
ISBN-10: 0-8218-1388-9
ISBN-13: 978-0-8218-1388-1
List Price: US$128
Member Price: US$102.40
Order Code: TRANS2/191
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The Theory Department of the Institute of Theoretical and Experimental Physics (ITEP) is internationally recognized for achievements in various branches of theoretical physics. The seminars at ITEP for many years have been among the main centers of scientific life in Moscow.

This volume presents results from the seminar on mathematical physics that has been held at ITEP since 1983. It reflects the style and direction of some of the work done at the Institute.

The majority of the papers in the volume describe the Knizhnik-Zamolodchikov-Bernard connection and its far-reaching generalizations. The remaining papers are related to other aspects of the theory and integrable models. Included are discussions on quantum Lax operators analyzed by methods of algebraic geometry, current algebras associated with complex curves, and the relationship between matrix models and integrable systems.

Readership

Graduate students and research mathematicians working in ordinary differential equations on manifolds and dynamical systems.

Table of Contents

  • G. E. Arutyunov, L. O. Chekhov, and S. A. Frolov -- Quantum dynamical \(R\)-matrices
  • B. Enriquez and V. Rubtsov -- Some examples of quantum groups in higher genus
  • V. V. Fock and A. A. Rosly -- Poisson structure on moduli of flat connections on Riemann surfaces and the \(r\)-matrix
  • D. A. Ivanov and A. S. Losev -- KZB equations as a flat connection with spectral parameter
  • S. Kharchev -- Kadomtsev-Petviashvili hierarchy and generalized Kontsevich model
  • S. Khoroshkin, D. Lebedev, and S. Pakuliak -- Yangian algebras and classical Riemann problems
  • I. Krichever and A. Zabrodin -- Vacuum curves of elliptic \(L\)-operators and representations of the Sklyanin algebra
  • A. M. Levin and M. A. Olshanetsky -- Hierarchies of isomonodromic deformations and Hitchin systems
  • N. Nekrasov -- Infinite-dimensional algebras, many-body systems and gauge theories
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