Dynamical $r$-matrices for the Elliptic Calogero-Moser Model

Abstract

For the integrable $N$-particle Calogero-Moser system with elliptic potential it is shown that the Lax operator found by Krichever possesses a classical $r$-matrix structure. The $r$-matrix is a natural generalisation of the matrix found recently by Avan and Talon (hep-th/9210128) for the trigonometric potential. The $r$-matrix depends on the spectral parameter and only half of the dynamical variables (particles' coordinates). It satisfies a generalized Yang-Baxter equation involving another dynamical matrix.

11p, LATEX file, LPTHE-93-42

References in corpus (4)

• Linear $r$-matrix algebra for classical separable systems
• Classical R-matrix structure for the Calogero model
• The Sine-Gordon Solitons as a N-Body Problem
• Construction of the classical $R$-matrices for the Toda and Calogero models

Cited by in corpus (21)

• Linear $r$-matrix algebra for classical separable systems
• $R$-matrices for Elliptic Calogero-Moser Models
• Separation of variables for the Ruijsenaars system
• Classical Poisson structures and r-matrices from constrained flows
• Characteristic Classes of SL(N)-Bundles and Quantum Dynamical Elliptic R-Matrices
• Spin Calogero models obtained from dynamical r-matrices and geodesic motion
• Characteristic Classes and Integrable Systems. General Construction
• Hitchin systems, higher Gaudin operators and $r$-matrices
• Separation of variables for A2 Ruijsenaars model and new integral representation for A2 Macdonald polynomials
• Liouville Integrability of Classical Calogero-Moser Models
• G(2)-Calogero-Moser Lax operators from reduction
• Quantum Twist-Deformed D=4 Phase Spaces with Spin Sector and Hopf Algebroid Structures
• Linear r-Matrix Algebra for a Hierarchy of One-Dimensional Particle Systems Separable in Parabolic Coordinates
• Spin Calogero models and dynamical r-matrices
• Spectral curve and Hamiltonian structure of isomonodromic SU(2) Calogero-Gaudin system
• On the r-matrix structure of the hyperbolic BC(n) Sutherland model
• On the classical r-matrix structure of the rational BC(n) Ruijsenaars-Schneider-van Diejen system
• On Classical r-Matrix for the Kowalevski Gyrostat on so(4)
• The nondynamical r-matrix structure of the elliptic Calogero-Moser model
• The nondynamical r-matrix structure for the elliptic $A_{n-1}$ Calogero-Moser model
• New Approach to the Integrability of the Calogero Models