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Regular version of the site

Article

Two-dimensional Riemann problem for rigid representations on an elliptic curve

Journal of Geometry and Physics. 2017. Vol. 114. P. 384-393.
Poberezhny V. A., Matveeva A.

We consider a generalization of Riemann–Hilbert problem on elliptic curves. For a given elliptic curve and irreducible representation of free group with two generators we construct explicitly a semistable vector bundle of degree zero obeying a logarithmic connection such that its monodromy over fundamental parallelogram is equivalent to given free group representation, monodromy along a−cycle is trivial and monodromy along b−cycle belong to certain orbit.