Rational Calogero-Moser Model: Explicit Form and r-Matrix of the Second Poisson Structure

TL;DR

This paper explicitly derives the second Poisson bracket structure for the rational Calogero-Moser model with 2 and 3 sites and introduces an r-matrix formulation for the N=2 case, connecting it to boundary algebra.

Contribution

It provides the explicit form of the second Poisson structure for small N and proposes an r-matrix formulation linking to boundary algebra, advancing understanding of the model's algebraic structure.

Findings

Explicit second Poisson brackets for N=2 and N=3

r-matrix formulation for N=2

Connection to classical limit of boundary algebra

Abstract

We compute the full expression of the second Poisson bracket structure for N=2 and N=3 site rational classical Calogero-Moser model. We propose an r-matrix formulation for N=2. It is identified with the classical limit of the second dynamical boundary algebra previously built by the authors.