R-matrices for elliptic Calogero-Moser models

• DOI: 10.1007/bf00939702
• Publication Date: 2005-01-02T04:40:58Z
• Authors: H. W. Braden; Takashi Suzuki
• Keywords: Elliptic flow; Momentum (technical analysis); Matrix (chemical analysis); Independence; Elliptic function

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.<br/>11 pages. Updated to agree with published version<br/>