A theorem gives sufficient conditions for an integrable system to descend through Poisson reduction, with explicit generalized action variables, applied to moduli spaces of flat connections and to the three doubles of compact Lie groups.
Vollmer, Torsion-free connections of second-order maximally superintegrable systems
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Integrable systems from Poisson reductions of generalized Hamiltonian torus actions
A theorem gives sufficient conditions for an integrable system to descend through Poisson reduction, with explicit generalized action variables, applied to moduli spaces of flat connections and to the three doubles of compact Lie groups.