Spin generalization of the Ruijsenaars-Schneider model, non-abelian 2D Toda chain and representations of Sklyanin algebra

@inproceedings{IKrichever1995SpinGO,
title={Spin generalization of the Ruijsenaars-Schneider model, non-abelian 2D Toda chain and representations of Sklyanin algebra},
author={I.Krichever and A.Zabrodin},
year={1995}
}

Action-angle type variables for spin generalizations of the elliptic Ruijsenaars-Schneider system are constructed. The equations of motion of these systems are solved in terms of Riemann theta-functions. It is proved that these systems are isomorphic to special elliptic solutions of the non-abelian 2D Toda chain. A connection between the finite gap solutions of solitonic equations and representations of the Sklyanin algebra is revealed and discrete analogs of the Lame operators are introduced… Expand