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Riemann–Hilbert for tame complex parahoric connections

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Abstract

A local Riemann–Hilbert correspondence for tame meromorphic connections on a curve compatible with a parahoric level structure will be established. Special cases include logarithmic connections on G-bundles and on parabolic G-bundles. The corresponding Betti data involves pairs (M, P) consisting of the local monodromy M ∈ G and a (weighted) parabolic subgroup P ⊂ G such that M ∈ P, as in the multiplicative Brieskorn–Grothendieck–Springer resolution (extended to the parabolic case). The natural quasi-Hamiltonian structures that arise on such spaces of enriched monodromy data will also be constructed.

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  1. École Normale Supérieure & CNRS, 45 rue d’Ulm, 75005, Paris, France

    P. P. Boalch

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Boalch, P.P. Riemann–Hilbert for tame complex parahoric connections. Transformation Groups 16, 27–50 (2011). https://doi.org/10.1007/s00031-011-9121-1

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