Deformations of Calogero-Moser Systems

Abstract

Recent results are surveyed pertaining to the complete integrability of some novel n-particle models in dimension one. These models generalize the Calogero-Moser systems related to classical root systems. Quantization leads to difference operators instead of differential operators.

4 pages, Latex (version 2.09), talk given at NEEDS '93, Gallipoli, Italy

References in corpus (1)

• Commuting difference operators with polynomial eigenfunctions

Cited by in corpus (23)

• Integrability of Conformal Blocks I: Calogero-Sutherland Scattering Theory
• Poisson-Lie interpretation of trigonometric Ruijsenaars duality
• The hyperbolic BC(n) Sutherland and the rational BC(n) Ruijsenaars-Schneider-van Diejen models: Lax matrices and duality
• On the Equilibrium Configuration of the BC-type Ruijsenaars-Schneider System
• Action-angle duality between the C(n)-type hyperbolic Sutherland and the rational Ruijsenaars-Schneider-van Diejen models
• The action-angle dual of an integrable Hamiltonian system of Ruijsenaars--Schneider--van Diejen type
• Duality between the trigonometric BC(n) Sutherland system and a completed rational Ruijsenaars-Schneider-van Diejen system
• Lax representation of the hyperbolic van Diejen dynamics with two coupling parameters
• Scattering theory of the hyperbolic BC(n) Sutherland and the rational BC(n) Ruijsenaars--Schneider--van Diejen models
• Integrable boundary interactions for Ruijsenaars' difference Toda chain
• The full phase space of a model in the Calogero-Ruijsenaars family
• On the scattering theory of the classical hyperbolic C(n) Sutherland model
• Trigonometric and elliptic Ruijsenaars-Schneider systems on the complex projective space
• Global description of action-angle duality for a Poisson-Lie deformation of the trigonometric ${\mathrm{BC}}_n$ Sutherland system
• On a Poisson-Lie deformation of the BC(n) Sutherland system
• Self-duality and scattering map for the hyperbolic van Diejen systems with two coupling parameters (with an appendix by S. Ruijsenaars)
• On the classical r-matrix structure of the rational BC(n) Ruijsenaars-Schneider-van Diejen system
• On the r-matrix structure of the hyperbolic BC(n) Sutherland model
• Integrable many-body systems of Calogero-Ruijsenaars type
• Equivalence of two sets of Hamiltonians associated with the rational BC(n) Ruijsenaars-Schneider-van Diejen system
• Stable equilibria for the roots of the symmetric continuous Hahn and Wilson polynomials
• Lax matrices for a 1-parameter subfamily of van Diejen--Toda chains
• On the derivation of Darboux form for the action-angle dual of trigonometric BC(n) Sutherland system