Integrable spin Calogero-Moser systems

Abstract

We introduce spin Calogero-Moser systems associated with root systems of simple Lie algebras and give the associated Lax representations (with spectral parameter) and fundamental Poisson bracket relations. The associated integrable models (called integrable spin Calogero-Moser systems in the paper) and their Lax pairs are then obtained via Poisson reduction and gauge transformations. For Lie algebras of $A_n$-type, this new class of integrable systems includes the usual Calogero-Moser systems as subsystems. Our method is guided by a general framework which we develop here using dynamical Lie algebroids.

30 pages, Latex file

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• Superintegrability of Calogero-Moser systems associated with the cyclic quiver
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• On the maximal superintegrability of strongly isochronous Hamiltonians
• On the bi-Hamiltonian structure of the trigonometric spin Ruijsenaars--Sutherland hierarchy