$R$-matrices for Elliptic Calogero-Moser Models

Abstract

The classical $R$-matrix structure for the $n$-particle Calogero-Moser models with (type IV) elliptic potentials is investigated. We show there is no momentum independent $R$-matrix (without spectral parameter) when $n\ge4$. The assumption of momentum independence is sufficient to reproduce the dynamical $R$-matrices of Avan and Talon for the type I,II,III degenerations of the elliptic potential. The inclusion of a spectral parameter enables us to find $R$-matrices for the general elliptic potential.