Riemann-Hilbert for tame complex parahoric connections

Details Riemann-Hilbert for tame complex parahoric connections Riemann-Hilbert for tame complex parahoric connections

2010-03-16

arxiv.org/abs/1003.3177v2

Transform. Groups 16 (2011), no. 1, 27-50

Mathematics

Differential Geometry

24 pages, minor improvements

Scientific paper

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, where G is a complex reductive group. The corresponding Betti data involves pairs (M,P) consisting of the local monodromy M in G and a (weighted) parabolic subgroup P of G such that M is in 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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