On the Schlesinger transformations of the sixth Painlevé equation (Q2721616)

By definition, Schlesinger transformations are discrete transformations that preserve the monodromy of Fuchsian systems and affinely transform the valuation of solutions in regular singular points. These transformations are transformations of Schlesinger isomonodromic equations. Fuchsian systems of second order corresponding to Schlesinger equations can be reduced to the Painlevé VI (P6) equation with four parameters. Schlesinger transformations act as birational transformations on solutions to P6 and as affine transformations in the space of its exponents (modification of initial parameter space). For earlier discovered Schlesinger transformations of the P6 (Fokas-Yortsos, Okamoto, Nijhoff-Joshi-Hone, Conte-Musette) and banal transformations (permutations of singular points, sign changes of exponents parameters), the author presents a list of relations among them.