Poisson geometry of parabolic bundles on Elliptic curves

Abstract

The moduli space of $G$-bundles on an elliptic curve with additional flag structure admits a Poisson structure. The bivector can be defined using double loop group, loop group and sheaf cohomology constructions. We investigate the links between these methods and for the case $\SL_2$ perform explicit computations, describing the bracket and its leaves in detail.

Final version: typos fixed, some re-organization; to appear IJM