Construction of a Fuchs equation with four given finite singular points and given reducible \(2 \times 2\) monodromy matrices (Q1649462)

The authors consider \(2\times 2\)-systems of Fuchsian linear differential equations on Riemann's sphere with four poles (three of which can be normalized to \(\pm 1\) and \(i\)) and with reducible monodromy groups. They explain how in the nonresonance case, given the monodromy group and the poles, one can construct the residua to obtain a Fuchsian system with the given poles and monodromy group.