Double Coset Construction of Moduli Space of Holomorphic Bundles and Hitchin Systems
Abstract
We present a description of the moduli space of holomorphic vector bundles over Riemann curves as a double coset space which is differ from the standard loop group construction. Our approach is based on equivalent definitions of holomorphic bundles, based on the transition maps or on the first order differential operators. Using this approach we present two independent derivations of the Hitchin integrable systems. We define a 'superfree`` upstairs system from which Hitchin systems are obtained by three step hamiltonian reductions. Special attention is given to the Schottky parameterization of curves.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 1997
 DOI:
 10.1007/s002200050173
 arXiv:
 arXiv:alggeom/9605005
 Bibcode:
 1997CMaPh.188..449L
 Keywords:

 Mathematics  Algebraic Geometry;
 High Energy Physics  Theory;
 14F05
 EPrint:
 19 pages, Latex