Differential Galois Theory and Isomonodromic Deformations
Copyright policy )Differential Galois Theory and Isomonodromic Deformations
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.
Mathematics - Differential Geometry, hypergeometric equation, 53C05, 14L30, 12H05, Group actions on varieties or schemes (quotients), [MATH.MATH-CV]Mathematics [math]/Complex Variables [math.CV], [MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA], Differential algebra, 530, [MATH.MATH-CA] Mathematics [math]/Classical Analysis and ODEs [math.CA], 510, differential Galois theory, Differential Geometry (math.DG), [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG], Mathematics - Classical Analysis and ODEs, [MATH.MATH-CV] Mathematics [math]/Complex Variables [math.CV], Classical Analysis and ODEs (math.CA), FOS: Mathematics, isomonodromic deformations, [MATH.MATH-DG] Mathematics [math]/Differential Geometry [math.DG], Connections (general theory)
Mathematics - Differential Geometry, hypergeometric equation, 53C05, 14L30, 12H05, Group actions on varieties or schemes (quotients), [MATH.MATH-CV]Mathematics [math]/Complex Variables [math.CV], [MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA], Differential algebra, 530, [MATH.MATH-CA] Mathematics [math]/Classical Analysis and ODEs [math.CA], 510, differential Galois theory, Differential Geometry (math.DG), [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG], Mathematics - Classical Analysis and ODEs, [MATH.MATH-CV] Mathematics [math]/Complex Variables [math.CV], Classical Analysis and ODEs (math.CA), FOS: Mathematics, isomonodromic deformations, [MATH.MATH-DG] Mathematics [math]/Differential Geometry [math.DG], Connections (general theory)
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