Differential Galois theory and isomonodromic deformations

David Blázquez-Sanz, Guy Casale, Juan Sebastián Díaz Arboleda

Published 2018-10-19Version 1

Here we present a geometric setting for the differential Galois theory of $G$-invariant connections with parameters. As an application of some classical results on differential algebraic groups and Lie algebra bundles, we see that the Galois group with parameters of a connection with simple $G$ is determined by its isomonodromic deformations. This allows us to compute the Galois groups with parameters of the general Fuchsian special linear system and of Gauss hypergeometric equation.