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arXiv · 1810.08566

Differential Galois Theory and Isomonodromic Deformations

David Blázquez Sanz·Guy Casale·Juan Sebastián Díaz Arboleda
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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.

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David Blázquez Sanz, Guy Casale, Juan Sebastián Díaz Arboleda. 2019-08-05. Differential Galois Theory and Isomonodromic Deformations. https://doi.org/10.3842/sigma.2019.055

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