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Superintegrable Systems on Moduli Spaces of Flat Connections

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arxiv 1909.08682 v1 pith:4OMZCNGR submitted 2019-09-18 math-ph math.MPnlin.SI

S. Arthamonov , N. Reshetikhin This is my paper · ORCID
classification math-phmath.MPnlin.SI
keywords modulisystemsconnectionsflatpoissonspacessuperintegrableatiyah-bott
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abstract

The main result of this paper is the construction of a family of superintegrable Hamiltonian systems on moduli spaces of flat connections on a principle $G$-bundle on a surface. The moduli space is a Poisson variety with Atiyah-Bott Poisson structure. Among particular cases of such systems are spin generalizations of Ruijsenaars-Schneider models.

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  1. Integrable systems from Poisson reductions of generalized Hamiltonian torus actions

    math-ph 2025-07 unverdicted novelty 7.0 of 10

    Develops sufficient conditions for Poisson reduction of generalized Hamiltonian torus actions to preserve integrability and applies them to open problems on Lie group doubles and flat-connection moduli spaces.

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