On the Galois group of some Fuchsian systems
type: Item
instance of: scholarly article
title: On the Galois group of some Fuchsian systems
zbMATH Open document ID: 1300.12007
author: A. Avoyan
published in: Journal of Mathematical Sciences (New York)
publication date: 2013-11-12T00:00:00Z
full work available at URL: https://arxiv.org/abs/1210.2433
review text: The author considers the system of linear differential equations of the form \[ df=\omega f,\tag{1} \] where \(\omega =\sum_{j=1}^{m}\frac{B_j}{z-a_j}dz,\;a_j\in \mathbb{C},\;B_j\in M_n(\mathbb{C})\) and \(\sum_{j=1}^{m}B_j=0\). He states that Theorem. Let system (1) be nonresonant. Then the differential Galois group is generated by \({e}^{2\pi i B_j}\). \(j=1,\dots ,m\). It is worth noting that it is immediately follow from the theorem that the Galois group of the system (1) does not depend on the relative position of singular points in the plane, what is somewhat unexpected.
Mathematics Subject Classification ID: 12H05
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 6225891
zbMATH Keywords: Galois group
zbMATH Keywords: Fuchsian system
zbMATH Keywords: monodromy group
reviewed by: Mykola Grygorenko
MaRDI profile type: Publication
OpenAlex ID: W1966164177
arXiv ID: 1210.2433
cites work: Q4869130
cites work: Regular systems on Riemann surfaces
cites work: Q4256615
cites work: Q4702207
cites work: Q4790565
DOI: 10.1007/S10958-013-1460-0
description: scientific article; zbMATH DE number 6225891