Differential Galois Theory and Isomonodromic Deformations

Symmetry Integrability and Geometry-Methods and Applications

article

David Blázquez Sanz¹  Guy Casale²  Juan Sebastián Díaz Arboleda¹ 

[1] Universidad Nacional de Colombia;Université de Rennes 1, Campus de Beaulieu

关键词: differential Galois theory;    isomonodromic deformations;    hypergeometric equation;   

DOI  :  10.3842/SIGMA.2019.055

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown