Abstract
We consider the canonical symplectic structure on the moduli space of flatg-connections on a Riemann surface of genusg withn marked points. Forg 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 ofn copies of Kirillov symplectic form on the orbit of dressing transformations in the Poisson-Lie groupG * andg copies of the symplectic structure on the Heisenberg double of the Poisson-Lie groupG (the pair (G, G *) corresponds to the Lie algebrag).
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Communicated by G. Felder
Supported by Swedish Natural Science Research Council (NFR) under the contract F-FU 06821-304
Supported in part by a Soros Foundation Grant awarded by the American Physical Society
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Alekseev, A.Y., Malkin, A.Z. Symplectic structure of the moduli space of flat connection on a Riemann surface. Commun.Math. Phys. 169, 99–119 (1995). https://doi.org/10.1007/BF02101598
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DOI: https://doi.org/10.1007/BF02101598