Liouville Integrability of a Class of Integrable Spin Calogero-Moser Systems and Exponents of Simple Lie Algebras

Abstract

In previous work, we introduced a class of integrable spin Calogero-Moser systems associated with the classical dynamical r-matrices with spectral parameter, as classified by Etingof and Varchenko for simple Lie algebras. Here the main purpose is to establish the Liouville integrability of these systems by a uniform method.