Two-dimensional Riemann problem for rigid representations on an elliptic curve. (English) Zbl 1361.35124
Summary: 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.
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