Differential Galois Theory and Isomonodromic Deformations

被引：1

作者：

Blazquez Sanz, David ^{[1
]}

Casale, Guy ^{[2
]}

Diaz Arboleda, Juan Sebastian ^{[1
]}

机构：

[1] Univ Nacl Colombia, Sede Medellin, Fac Ciencias, Escuela Matemat, Calle 59A 63-20, Medellin, Antioquia, Colombia

[2] Univ Rennes 1, IRMAR, Campus Beaulieu,Bat 22-23,263 Ave Gen Leclerc, F-35042 Rennes, France

来源：

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2019年 / 15卷

关键词：

differential Galois theory; isomonodromic deformations; hypergeometric equation; PICARD-VESSIOT EXTENSIONS; ALGEBRAIC-GROUPS; EQUATIONS;

D O I：

10.3842/SIGMA.2019.055

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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.

引用

页数：35

共 27 条

[1]

[Anonymous], 1973, PURE APPL MATH

[2] On the computation of the parameterized differential Galois group for a second-order linear differential equation with differential parameters [J].