Painlevé equations and the middle convolution

Titelangaben

Dettweiler, Michael ; Reiter, Stefan:
Painlevé equations and the middle convolution.
In: Advances in Geometry. Bd. 7 (2007) Heft 3 . - S. 317-330.
ISSN 1615-7168
DOI: https://doi.org/10.1515/ADVGEOM.2007.019

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Abstract

We relate the theory of the middle convolution functor MC λ to the study of algebraic solutions of the sixth Painlevé equation PVI. We interpret some recently found algebraic solutions by Boalch in terms of the middle convolution. Then we show how to obtain algebraic solutions of PVI by starting with triples in GL 2 and applying MC λ . The effect on the underlying Fuchsian systems can be described in a very simple manner.