This article is cited in 1 paper

Differential Galois Theory and Isomonodromic Deformations

David Blázquez-Sanz^a, Guy Casale^b, Juan Sebastián Díaz Arboleda<sup>a

a</sup> Universidad Nacional de Colombia, Sede Medellín, Facultad de Ciencias, Escuela de Matemáticas, Calle 59A No. 63 - 20, Medellín, Antioquia, Colombia
^b IRMAR, Université de Rennes 1, Campus de Beaulieu, bât. 22-23, 263 avenue du Général Leclerc, CS 74205, 35042 RENNES Cedex, France

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.

Keywords: differential Galois theory, isomonodromic deformations, hypergeometric equation.

MSC: 53C05, 14L30, 12H05

Received: November 14, 2018; in final form July 29, 2019; Published online August 5, 2019

Language: English

DOI: 10.3842/SIGMA.2019.055

Bibliographic databases:

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ArXiv: 1810.08566