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 grou...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2019
Main Authors: Blázquez Sanz, D., Casale, G., Díaz Arboleda, J.S.
Format: Article
Language:English
Published: Інститут математики НАН України 2019
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/210240
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Differential Galois Theory and Isomonodromic Deformations / D. Blázquez Sanz, G. Casale, J.S. Díaz Arboleda // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 27 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-210240
record_format dspace
spelling Blázquez Sanz, D.
Casale, G.
Díaz Arboleda, J.S.
2025-12-04T13:08:57Z
2019
Differential Galois Theory and Isomonodromic Deformations / D. Blázquez Sanz, G. Casale, J.S. Díaz Arboleda // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 27 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 53C05; 14L30; 12H05
arXiv: 1810.08566
https://nasplib.isofts.kiev.ua/handle/123456789/210240
https://doi.org/10.3842/SIGMA.2019.055
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 the Gauss hypergeometric equation.
We would like to thank the Université de Rennes 1 and the Universidad Nacional de Colombia for their hospitality and support. 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 the Math-AMSUD project "Complex Geometry and Foliations". J.S. Díaz Arboleda is partially funded by the Colciencias program 647 "Doctorados Nacionales". D. Blázquez Sanz specially thanks the support, care, and patience of D. Higuita during the writing process.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Differential Galois Theory and Isomonodromic Deformations
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title Differential Galois Theory and Isomonodromic Deformations
spellingShingle Differential Galois Theory and Isomonodromic Deformations
Blázquez Sanz, D.
Casale, G.
Díaz Arboleda, J.S.
title_short Differential Galois Theory and Isomonodromic Deformations
title_full Differential Galois Theory and Isomonodromic Deformations
title_fullStr Differential Galois Theory and Isomonodromic Deformations
title_full_unstemmed Differential Galois Theory and Isomonodromic Deformations
title_sort differential galois theory and isomonodromic deformations
author Blázquez Sanz, D.
Casale, G.
Díaz Arboleda, J.S.
author_facet Blázquez Sanz, D.
Casale, G.
Díaz Arboleda, J.S.
publishDate 2019
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
description 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 the Gauss hypergeometric equation.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/210240
citation_txt Differential Galois Theory and Isomonodromic Deformations / D. Blázquez Sanz, G. Casale, J.S. Díaz Arboleda // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 27 назв. — англ.
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first_indexed 2025-12-07T21:24:52Z
last_indexed 2025-12-07T21:24:52Z
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