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

1993/12/01 by Anton Alekseev, A. Yu. Alekseev, Anton Malkin +1 · 4 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #hep-th #math.DG

paper · pdf · doi:10.1007/bf02101598

published as Commun.Math.Phys.169:99-120,1995 · 20 pages

arxiv created 1993/12/01 · openalex publication_date 1995/04/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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^* 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).

Citations

• On quantum group symmetries of conformal field theories

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