We give fundamental solutions of arbitrarily sized matrix Fuchsian linear systems, in the case where the coefficients B^ (i) of the systems are matrix solutions of the Schlesinger system that are upper triangular, and whose eigenvalues follow an arithmetic progression of a rational difference. The values on the superdiagonals of the matrices B^ (i) are given by contour integrals of meromorphic differentials defined on Riemann surfaces obtained by compactification of superelliptic curves.
Ghabra et al. (Mon,) studied this question.