Develops sufficient conditions for integrable systems to descend under Poisson reductions of generalized Hamiltonian torus actions, with applications to systems on doubles of compact Lie groups and moduli spaces of flat connections.
Degenerate Integrability of Spin Calogero-Moser Systems and the duality with the spin Ruijsenaars systems
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abstract
It is shown that spin Calogero-Moser systems are completely integrable in a sense of degenerate integrability. Their Liouville tori have dimension less then half of the dimension of the phase space. It is also shown that rational spin Ruijsenaars systems are degenerately integrable and dual to spin Calogero- Moser systems in a sense that action-algle variables of one are angle-action variables of the other.
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2025 1verdicts
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Integrable systems from Poisson reductions of generalized Hamiltonian torus actions
Develops sufficient conditions for integrable systems to descend under Poisson reductions of generalized Hamiltonian torus actions, with applications to systems on doubles of compact Lie groups and moduli spaces of flat connections.