Calogero—Moser— Sutherland Models

1. Front Matter

   Pages i-xxv

   PDF

2. Classical Dynamical r-Matrices for Calogero—Moser Systems and Their Generalizations

   • J. Avan

   Pages 1-21

3. Hidden Algebraic Structure of the Calogero—Sutherland Model, Integral Formula for Jack Polynomial and Their Relativistic Analog

   • Hidetoshi Awata

   Pages 23-35

4. Polynomial Eigenfunctions of the Calogero—Sutherland—Moser Models with Exchange Terms

   • T. H. Baker, C. F. Dunkl, P. J. Forrester

   Pages 37-51

5. The Theory of Lacunas and Quantum Integrable Systems

   • Yuri Yu. Berest

   Pages 53-64

6. Canonical Forms for the C-Invariant Tensors

   • Oleg I. Bogoyavlenskij

   Pages 65-76

7. R-Matrices, Generalized Inverses, and Calogero—Moser—Sutherland Models

   • H. W. Braden

   Pages 77-92

8. Tricks of the Trade: Relating and Deriving Solvable and Integrable Dynamical Systems

   • Francesco Calogero

   Pages 93-116

9. Classical and Quantum Partition Functions of the Calogero—Moser—Sutherland Model

   • Ph. Choquard

   Pages 117-125

10. The Meander Determinant and Its Generalizations

    • P. Di Francesco

    Pages 127-144

11. Differential Equations for Multivariable Hermite and Laguerre Polynomials

    • J. F. van Diejen

    Pages 145-159

12. Quantum Currents Realization of the Elliptic Quantum Groups E _τ,η(sl₂)

    • B. Enriquez

    Pages 161-176

13. Heisenberg—Ising Spin Chain: Plancherel Decomposition and Chebyshev Polynomials

    • Eugene Gutkin

    Pages 177-192

14. Ruijsenaars’s Commuting Difference System from Belavin’s Elliptic R-Matrix

    • Koji Hasegawa

    Pages 193-202

15. Invariants and Eigenvectors for Quantum Heisenberg Chains with Elliptic Exchange

    • V. I. Inozemtsev

    Pages 203-220

16. The Bispectral Involution as a Linearizing Map

    • Alex Kasman

    Pages 221-229

17. On Some Quadratic Algebras: Jucys—Murphy and Dunkl Elements

    • Anatol N. Kirillov

    Pages 231-248

18. Elliptic Solutions to Difference Nonlinear Equations and Nested Bethe Ansatz Equations

    • I. Krichever

    Pages 249-271

19. Creation Operators for the Calogero—Sutherland Model and Its Relativistic Version

    • Luc Lapointe, Luc Vinet

    Pages 273-297

20. New Exact Results for Quantum Impurity Problems

    • F. Lesage, H. Saleur, P. Simonetti

    Pages 299-312

In the 1970s F. Calogero and D. Sutherland discovered that for certain potentials in one-dimensional systems, but for any number of particles, the Schrödinger eigenvalue problem is exactly solvable. Until then, there was only one known nontrivial example of an exactly solvable quantum multi-particle problem. J. Moser subsequently showed that the classical counterparts to these models is also amenable to an exact analytical approach. The last decade has witnessed a true explosion of activities involving Calogero-Moser-Sutherland models, and these now play a role in research areas ranging from theoretical physics (such as soliton theory, quantum field theory, string theory, solvable models of statistical mechanics, condensed matter physics, and quantum chaos) to pure mathematics (such as representation theory, harmonic analysis, theory of special functions, combinatorics of symmetric functions, dynamical systems, random matrix theory, and complex geometry). The aim of this volume is to provide an overview of the many branches into which research on CMS systems has diversified in recent years. The contributions are by leading researchers from various disciplines in whose work CMS systems appear, either as the topic of investigation itself or as a tool for further applications.

• Potential
• chaos
• differential equation
• dynamical system
• dynamical systems
• eigenvalue
• field theory
• invariant
• quantum chaos
• quantum field theory
• solution
• statistical mechanics
• tensor
• theoretical physics
• thermodynamics

• Departamento de Matematicas, Universidad de Chile, Nunoa Santiago, Chile

  Jan Felipe Diejen

• McGill University, Montreal, Canada

  Luc Vinet

Policies and ethics