Title: Spin generalization of the Ruijsenaars-Schneider model, the non-Abelian 2D Toda chain, and representations of the Sklyanin algebra
Abstract: 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 thetafunctions.It is proved that these systems are isomorphic to special elliptic solutions of the nonabelian 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.A simple way to construct representations of the Sklyanin algebra by difference operators is suggested.