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.
Superintegrability of Generalized Toda Models on Symmetric Spaces
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abstract
In this paper we prove superintegrability of Hamiltonian systems generated by functions on $K\backslash G/K$, restriced to a symplectic leaf of the Poisson variety $G/K$, where $G$ is a simple Lie group with the standard Poisson Lie structure, $K$ is the subgroup of fixed points with respect to the Cartan involution.
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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.