SYMPLECTIC STRUCTURE OF THE MODULI SPACE OF FLAT CONNECTION ON A RIEMANN SURFACE

We consider the canonical symplectic structure on the moduli space of flat g-connections on a Riemann surface of genus g with a marked point s. For a being a semisimple Lie algebra we obtain an explicit efficien t formula for this symplectic form and prove that it may be represente d as a sum of a copies of Kirillov symplectic form on the orbit of dre ssing transformations in the Poisson-Lie group G and g copies of the symplectic structure on the Heisenberg double of the Poisson-Lie group G (the pair (G,G) corresponds to the Lie algebra g).