Calogero–Sutherland system with two types interacting spins


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We consider the classical Calogero–Sutherland system with two types of interacting spin variables. It can be reduced to the standard Calogero–Sutherland system, when one of the spin variables vanishes. We describe the model in the Hitchin approach and prove complete integrability of the system by constructing the Lax pair and the classical r-matrix with the spectral parameter on a singular curve.

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S. Kharchev

Institute for Theoretical and Experimental Physics; Institute for Information Transmission Problems (Kharkevich Institute)

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Email: kharchev@itep.ru
俄罗斯联邦, Moscow, 117218; Moscow, 127994

A. Levin

Institute for Theoretical and Experimental Physics; International Laboratory for Mirror Symmetry and Automorphic Forms, Faculty of Mathematics

Email: kharchev@itep.ru
俄罗斯联邦, Moscow, 117218; Moscow, 119048

M. Olshanetsky

Institute for Theoretical and Experimental Physics; Institute for Information Transmission Problems (Kharkevich Institute)

Email: kharchev@itep.ru
俄罗斯联邦, Moscow, 117218; Moscow, 127994

A. Zotov

Institute for Theoretical and Experimental Physics; Steklov Mathematical Institute

Email: kharchev@itep.ru
俄罗斯联邦, Moscow, 117218; Moscow, 119991

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