Calogero-Moser systems for simple Lie groups and characteristic classes of bundles

摘要

This paper is a continuation of our paper Levin et al. [1]. We consider Modified Calogero-Moser (CM) systems corresponding to the Higgs bundles with an arbitrary characteristic class over elliptic curves. These systems are generalization of the classical Calogero-Moser systems with spin related to simple Lie groups and contain CM subsystems related to some (unbroken) subalgebras. For all algebras we construct a special basis, corresponding to non-trivial characteristic classes, the explicit forms of Lax operators and quadratic Hamiltonians. As by product, we describe the moduli space of stable holomorphic bundles over elliptic curves with arbitrary characteristic classes.