A one-dimensional many-body integrable model from $Z_n$ Belavin model with open boundary conditions

Abstract

We use factorized $L$ operator to construct an integrable model with open boundary conditions. By taking trigonometic limit($τ\to \sqrt{-1}\infty$) and scaling limit($ω\to 0$), we get a Hamiltonian of a classical integrable system. It shows that this integrable system is similar to those found by Calogero et al.