Symplectic structure of the moduli space of flat connections on a Riemann surface

Abstract

We consider canonical symplectic structure on the moduli space of flat ${\g}$-connections on a Riemann surface of genus $g$ with $n$ marked points. For ${\g}$ being a semisimple Lie algebra we obtain an explicit efficient formula for this symplectic form and prove that it may be represented as a sum of $n$ copies of Kirillov symplectic form on the orbit of dressing transformations in the Poisson-Lie group $G^{\ast }$ and $g$ copies of the symplectic structure on the Heisenberg double of the Poisson-Lie group $G$ (the pair ($G,G^{\ast }$) corresponds to the Lie algebra ${\g}$).

20 pages

References in corpus (1)

• Symplectic structures associated to Lie-Poisson groups

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