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.
Poisson-Lie interpretation of trigonometric Ruijsenaars duality
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abstract
A geometric interpretation of the duality between two real forms of the complex trigonometric Ruijsenaars-Schneider system is presented. The phase spaces of the systems in duality are viewed as two different models of the same reduced phase space arising from a suitable symplectic reduction of the standard Heisenberg double of U(n). The collections of commuting Hamiltonians of the systems in duality are shown to descend from two families of `free' Hamiltonians on the double which are dual to each other in a Poisson-Lie sense. Our results give rise to a major simplification of Ruijsenaars' proof of the crucial symplectomorphism property of the duality map.
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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.