Matrix Riemann-hilbert Problems Related to Branched Coverings of Cp1
نویسنده
چکیده
In these notes we solve a class of Riemann-Hilbert (inverse monodromy) problems with an arbitrary quasi-permutation monodromy group. The solution is given in terms of Szegö kernel on the underlying Riemann surface. In particular, our construction provides a new class of solutions of the Schlesinger system. We present some results on explicit calculation of the corresponding tau-function, and describe divisor of zeros of the tau-function (so-called Malgrange divisor) in terms of the theta-divisor on the Jacobi manifold of the Riemann surface. We discuss the relationship of the tau-function to determinant of Laplacian operator on the Riemann surface.
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