Duke Mathematical Journal

Quasi-Hamiltonian geometry of meromorphic connections

Philip Boalch

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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 disk, and they generalise the conjugacy class example of Alekseev, Malkin, and Meinrenken [3] (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

Article information

Duke Math. J., Volume 139, Number 2 (2007), 369-405.

First available in Project Euclid: 31 July 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53D30: Symplectic structures of moduli spaces 34M40: Stokes phenomena and connection problems (linear and nonlinear)
Secondary: 22E67: Loop groups and related constructions, group-theoretic treatment [See also 58D05]


Boalch, Philip. Quasi-Hamiltonian geometry of meromorphic connections. Duke Math. J. 139 (2007), no. 2, 369--405. doi:10.1215/S0012-7094-07-13924-3. https://projecteuclid.org/euclid.dmj/1185891826

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