Superintegrable Systems on Moduli Spaces of Flat Connections

TL;DR

This paper constructs a family of superintegrable Hamiltonian systems on moduli spaces of flat connections, including spin generalizations of Ruijsenaars-Schneider models, revealing new integrable structures in geometric representation theory.

Contribution

It introduces novel superintegrable systems on moduli spaces of flat connections, expanding the class of known integrable models with geometric and physical significance.

Findings

Constructed superintegrable Hamiltonian systems on moduli spaces.

Identified spin generalizations of Ruijsenaars-Schneider models.

Demonstrated the Poisson structure compatibility of these systems.

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.