Computation of RS-pullback transformations for algebraic Painlevé VI solutions
نویسندگان
چکیده
Algebraic solutions of the sixth Painlevé equation can be computed using pullback transformations of hypergeometric equations with respect to specially ramified rational coverings. In particular, as was noticed by the second author and Doran, some algebraic solutions can be constructed from a rational covering alone, without computation of the pullbacked Fuchsian equation. But the same covering can be used to pullback different hypergeometric equations, resulting in different algebraic Painlevé VI solutions. This paper presents computations of explicit RS-pullback transformations, and derivation of algebraic Painlevé VI solutions from them. As an example, we present computation of all seed solutions for pull-backs of hyperbolic hypergeometric systems. 2000 Mathematics Subject Classification: 34M55, 33E17, 57M12. Short title: RS-pullback transformations
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