$R$-matrices for the $n=2,3$ Elliptic Calogero-Moser Models

Abstract

The classical (dynamical) $R$-matrices for the 2- and 3-body Calogero-Moser models with elliptic potentials are given. The 3-body case has an interesting nontrivial structure that goes beyond the known ansatz for momentum independent $R$-matrices. The $R$-matrices presented include the dynamical $R$-matrices of Avan and Talon as degenerate cases of the elliptic potential.

References in corpus (3)

• Exchange Operator Formalism for Integrable Systems of Particles
• Explicit Solution to the N-Body Calogero Problem
• Classical R-matrix structure for the Calogero model

Cited by in corpus (3)

• Classical R-Matrices and the Feigin-Odesskii Algebra via Hamiltonian and Poisson Reductions
• The Classical $r$-Matrix for the Relativistic Ruijsenaars-Schneider System
• On Calogero-Francoise-type Lax matrices and their dynamical r-matrices