  In these notes we solve a class of Riemann-Hilbert (inverse monodromy)
problems with quasi-permutation monodromy groups which correspond to
non-singular branched coverings of $\CP1$. The solution is given in terms of
Szeg\"o 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.
