A note on pseudo-CM representations and differential Galois groups
Let G be a linear algebraic group, with \(G^ 0\) as connected component through the identity, and let V be a representation of G which is \(G^ 0\)-irreducible. In the first part of this paper, the authors show that the existence of a ``sufficiently well spread'' torus in G ensures that \(G^ 0\) is a product of groups of SL, Sp or SO type. The proof is based on a generalization of the study of ``cyclically-minuscule'' representations of Lie algebras given by the first author in Invent. Math. 87, 13-61 (1987; Zbl 0609.12025)]. In the second part, the authors apply their criterion to the computation of the differential Galois group of certain differential equations L on \({\mathbb{G}}_ m\), all of whose determining factors at infinity present similar type of ramifications (this condition implies that L is irreducible over \({\mathbb{G}}_ m).\) [See also the paper by \textit{N. M. Katz} in Duke Math. J. 54, 41-56 (1987; review 12004).]
scientific article; zbMATH DE number 4047842