  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.
