Double coset construction of moduli space of holomorphic bundles and Hitchin systems

Details Double coset construction of moduli space of holomorphic bundles and Hitchin systems Double coset construction of moduli space of holomorphic bundles and Hitchin systems

1996-05-13

arxiv.org/abs/alg-geom/9605005v1

Commun.Math.Phys. 188 (1997) 449-466

Physics

High Energy Physics

High Energy Physics - Theory

19 pages, Latex

Scientific paper

10.1007/s002200050173

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 systems from which Hitchin systems are obtained by three step hamiltonian reductions. A special attention is being given on the Schottky parameterization of curves.

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