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Quasi-Hamiltonian Geometry of Meromorphic Connections

Philip Boalch
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Abstract

For each connected complex reductive group G, we find a family of new examples of complex quasi-Hamiltonian G-spaces with G-valued moment maps. These spaces arise naturally as moduli spaces of (suitably framed) meromorphic connections on principal G-bundles over a disc, and they generalise the conjugacy class example of Alekseev, Malkin and Meinrenken (which appears in the simple pole case). Using the `fusion product' in the theory this gives a finite dimensional construction of the natural symplectic structures on the spaces of monodromy/Stokes data of meromorphic connections over arbitrary genus Riemann surfaces, together with a new proof of the symplectic nature of isomonodromic deformations of such connections.

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Philip Boalch. 2002-03-15. Quasi-Hamiltonian Geometry of Meromorphic Connections. https://doi.org/10.1215/s0012-7094-07-13924-3

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