Superintegrable Systems on Moduli Spaces of Flat Connections

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.

References in corpus (3)

• Poisson Geometry of SL(3,C)-Character Varieties Relative to a Surface with Boundary
• Continuous tensor categories from quantum groups I: algebraic aspects
• Dual generators of the fundamental group and the moduli space of flat connections

Cited by in corpus (5)

• Poisson reductions of master integrable systems on doubles of compact Lie groups
• Integrable systems on multiplicative quiver varieties from cyclic quivers
• Reduction of divisors for classical superintegrable $GL(3)$ magnetic chain
• Graphical calculus for quantum vertex operators, I: The dynamical fusion operator
• Bi-Hamiltonian structure of Sutherland models coupled to two $\mathfrak{u}(n{)}^{\ast }$-valued spins from Poisson reduction