Differential Galois Theory and Isomonodromic Deformations

Abstract

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 of a connection with parameters with simple structural group $G$ 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.

References in corpus (2)

• On parameterized differential Galois extensions
• Parallelisms & Lie Connections