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 |
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| Date: | 2019 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2019
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| 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 |
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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. |
| work_keys_str_mv |
AT blazquezsanzd differentialgaloistheoryandisomonodromicdeformations AT casaleg differentialgaloistheoryandisomonodromicdeformations AT diazarboledajs differentialgaloistheoryandisomonodromicdeformations |
| first_indexed |
2025-12-07T21:24:52Z |
| last_indexed |
2025-12-07T21:24:52Z |
| _version_ |
1850886263602675712 |