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Action-angle type variables for spin generalizations of the ellipticRuijsenaars-Schneider system are constructed. The equations of motion of thesesystems are solved in terms of Riemann theta-functions. It is proved that thesesystems are isomorphic to special elliptic solutions of the non-abelian 2D Todachain. A connection between the finite gap solutions of solitonic equations andrepresentations of the Sklyanin algebra is revealed and discrete analogs of theLame operators are introduced. A simple way to construct representations of theSklyanin algebra by difference operators is suggested.Comment: 38 pages, latex, no figure

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