2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/57425In this paper we solve an arbitrary matrix Riemann-Hilbert (inverse monodromy) problem with quasi-permutation monodromy representations outside of a divisor in the space of monodromy data. This divisor is characterized in terms of the theta-divisor on the Jacobi manifold of an auxiliary compact Riemann surface realized as an appropriate branched covering of $\CP1$ . The solution is given in terms of a generalization of Szegö kernel on the Riemann surface. In particular, our construction provides a new class of solutions of the Schlesinger system. The isomonodromy tau-function of these solutions is computed up to a nowhere vanishing factor independent of the elements of monodromy matrices.submitted to Math.Annalen 08.2002Mathematical PhysicsExactly Solvable and Integrable Systemstext