Differential Galois Theory and Isomonodromic Deformations

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

Symmetry, integrability and geometry: methods and applications, Tome 15 (2019)

Résumé

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.

Détail

Keywords: differential Galois theory, hypergeometric equation.
Mots-clés : isomonodromic deformations

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