CalogeroMoser systems for simple Lie groups and characteristic classes of bundles
Abstract
This paper is a continuation of our paper Levin et al. [1]. We consider Modified CalogeroMoser (CM) systems corresponding to the Higgs bundles with an arbitrary characteristic class over elliptic curves. These systems are generalization of the classical CalogeroMoser 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 nontrivial 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.
 Publication:

Journal of Geometry and Physics
 Pub Date:
 August 2012
 DOI:
 10.1016/j.geomphys.2012.03.012
 arXiv:
 arXiv:1004.3163
 Bibcode:
 2012JGP....62.1810L
 Keywords:

 Mathematics  Symplectic Geometry;
 High Energy Physics  Theory;
 Mathematical Physics;
 Mathematics  Differential Geometry;
 Mathematics  Quantum Algebra
 EPrint:
 33 pages