Schlesinger transformations for algebraic Painleve VI solutions

Abstract

Various Schlesinger transformations can be combined with a direct pull-back of a hypergeometric 2x2 system to obtain $R{S}_4^2$-pullback transformations to isomonodromic 2x2 Fuchsian systems with 4 singularities. The corresponding Painleve VI solutions are algebraic functions, possibly in different orbits under Okamoto transformations. This paper demonstrates a direct computation of Schlesinger transformations acting on several apparent singular points, and presents an algebraic procedure (via syzygies) of computing algebraic Painleve VI solutions without deriving full RS-pullback transformations.

26 pages

References in corpus (4)

• Transformations ${RS}_4^2(3)$ of the Ranks $\le 4$ and Algebraic Solutions of the Sixth Painlevé Equation
• Some explicit solutions to the Riemann-Hilbert problem
• Computation of highly ramified coverings
• Special Functions of the Isomonodromy Type, Rational Transformations of Spectral Parameter, and Algebraic Solutions of the Sixth Painlevé Equation

Cited by in corpus (2)

• Middle Convolution and Heun's Equation
• Computation of RS-pullback transformations for algebraic Painleve VI solutions