Spin generalization of the Ruijsenaars-Schneider model, non-abelian 2D Toda chain and representations of 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 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. A simple way to construct representations of the Sklyanin algebra by difference operators is suggested.

38 pages, latex, no figures

References in corpus (3)

• Hamiltonian systems of Calogero type and two dimensional Yang-Mills theory
• Elliptic Calogero-Moser system from two dimensional current algebra
• Bethe Ansatz for higher spin eight vertex models

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