On the Galois group of some Fuchsian systems
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.
scientific article; zbMATH DE number 6225891