The trigonometric spin Ruijsenaars-Sutherland hierarchy is obtained by Poisson reduction of a bi-Hamiltonian free system on T*U(n), yielding explicit compatible reduced Poisson brackets.
Integrable spin Calogero-Moser systems
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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.
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2019 1verdicts
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Reduction of a bi-Hamiltonian hierarchy on $T^*\mathrm{U}(n)$ to spin Ruijsenaars--Sutherland models
The trigonometric spin Ruijsenaars-Sutherland hierarchy is obtained by Poisson reduction of a bi-Hamiltonian free system on T*U(n), yielding explicit compatible reduced Poisson brackets.