Titre : Integrable systems associated with elliptic algebras and beyond.

Résumé :

We construct some new Integrable Systems (IS) both classical and quantum associated with elliptic algebras. Our constructions are partly based on the algebraic integrability mechanism given by the existence of commuting families in skew fields and partly - on the internal properties of the elliptic algebras and their representations. Among the examples of such IS are Beauville-Mukai systems, Felder-Varchenko antiperiodic IRF models, differential-difference many-particle hamiltonian systems and Seiberg-Witten IS.

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