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Generalized Classical Dynamical Yang-Baxter Equations and Moduli Spaces of Flat Connections on Surfaces

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Abstract

In this paper, we explain how generalized dynamical r-matrices can be obtained by (quasi-)Poisson reduction. New examples of Poisson structures, Poisson G-spaces and Poisson groupoid actions naturally appear in this setting. As an application, we use a generalized dynamical r-matrix, induced by the gauge fixing procedure, to give a new finite dimensional description of the Atiyah-Bott symplectic structure on the moduli space of flat connections on a surface. Using this, we find a Poisson groupoid symmetry of the moduli space.

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Authors and Affiliations

  1. Section of Mathematics, University of Geneva, 2-4 Rue de Lièvre, c.p. 64, 1211, Geneva 4, Switzerland

    Xiaomeng Xu

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  1. Xiaomeng Xu
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Correspondence to Xiaomeng Xu.

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Communicated by N. Reshetikhin

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Xu, X. Generalized Classical Dynamical Yang-Baxter Equations and Moduli Spaces of Flat Connections on Surfaces. Commun. Math. Phys. 341, 523–542 (2016). https://doi.org/10.1007/s00220-015-2533-3

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  • DOI: https://doi.org/10.1007/s00220-015-2533-3

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