Quasi-Hamiltonian Geometry of Meromorphic Connections

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.

21 pages

References in corpus (3)

• Symplectic Manifolds and Isomonodromic Deformations
• Stokes Matrices and Poisson Lie Groups
• The symplectic and twistor geometry of the general isomonodromic deformation problem

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