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19 January 2021
  » arxiv » hep-th/9312004

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Symplectic structure of the moduli space of flat connections on a Riemann surface
A. Yu. Alekseev ; A. Z. Malkin ;
Date 1 Dec 1993
Journal Commun.Math.Phys. 169 (1995) 99
Subject High Energy Physics - Theory; Differential Geometry | hep-th math.DG
AbstractWe 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 $G^{*}$ 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 ${g}$).
Source arXiv, hep-th/9312004
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