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Symmetry, Integrability and Geometry: Methods and Applications, 2019, Volume 15, 055, 35 pp.
DOI: https://doi.org/10.3842/SIGMA.2019.055 (Mi sigma1491) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Differential Galois Theory and Isomonodromic Deformations

David Blázquez-Sanza, Guy Casaleb, Juan Sebastián Díaz Arboledaa

a 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
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DOI: https://doi.org/10.3842/SIGMA.2019.055
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.
Funding agency Grant number
Departamento Administrativo de Ciencia, Tecnología e Innovación 776-2017 code 57708 (Hermes UN 38300)
647 “Doctorados Nacionales”
D. Blázquez-Sanz is partially funded by Colciencias project “Estructuras lineales en geometría y topología” 776-2017 code 57708 (Hermes UN 38300). G. Casale is partially funded by Math-AMSUD project “Complex Geometry and Foliations”. J.S. Díaz Arboleda is partially funded by Colciencias program 647 “Doctorados Nacionales”.
Received: November 14, 2018; in final form July 29, 2019; Published online August 5, 2019
Bibliographic databases:
Document Type: Article
MSC: 53C05, 14L30, 12H05
Language: English
Citation: David Blázquez-Sanz, Guy Casale, Juan Sebastián Díaz Arboleda, “Differential Galois Theory and Isomonodromic Deformations”, SIGMA, 15 (2019), 055, 35 pp.
Citation in format AMSBIB
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\paper Differential Galois Theory and Isomonodromic Deformations
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\vol 15
\papernumber 055
\totalpages 35
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
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