Integrability in the Hamiltonian Сhern–Simons theory

We consider the moduli space of flat connections on the Riemann surface with marked points. The new efficient parametrization is suggested and used to construct an integrable model on the moduli space. A family of commuting Hamiltonians is extracted from the trace of the transfer matrix built from the Wilson line observables of the Chern–Simons theory. Our model appears to be gauge equivalent to XXZ magnetic chain with finite number of sites.