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

TL;DR

This paper derives explicit classical dynamical R-matrices for 2- and 3-body elliptic Calogero-Moser models, revealing complex structures beyond known ansatzes and unifying degenerate cases.

Contribution

It provides new explicit R-matrices for elliptic Calogero-Moser models, especially highlighting the nontrivial 3-body case beyond existing frameworks.

Findings

Explicit R-matrices for 2- and 3-body models derived.

3-body R-matrix exhibits complex structure beyond known ansatz.

Degenerate cases recover known R-matrices of Avan and Talon.

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.