Reduction of Schlesinger Systems to Linear Jordan–Pochhammer Systems

We study the reducibility of an isomonodromic family of Fuchsian systems on the Riemann sphere which is determined by some initial Fuchsian system and its monodromy to an isomonodromic family of upper triangular Fuchsian systems. Under some conditions on the monodromy of the initial Fuchsian system, a nonlinear Schlesinger system is reduced to a system of homogeneous and inhomogeneous linear Pfaffian Jordan–Pochhammer differential equations. Such Jordan–Pochhammer systems possess hypergeometric type solutions admitting an explicit description of their integral representations.