A note on pseudo-CM representations and differential Galois groups
type: Item
instance of: scholarly article
title: A note on pseudo-CM representations and differential Galois groups
zbMATH Open document ID: 0643.12007
DOI: 10.1215/S0012-7094-87-05405-6
author: Nicholas M. Katz
author: Richard Pink
published in: Duke Mathematical Journal
publication date: 1987-01-01T00:00:00Z
review text: 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).]
Mathematics Subject Classification ID: 12H20
Mathematics Subject Classification ID: 17B45
Mathematics Subject Classification ID: 34M99
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 17B10
zbMATH DE Number: 4047842
zbMATH Keywords: monodromy
zbMATH Keywords: representations of Lie algebras
zbMATH Keywords: differential Galois group
reviewed by: Daniel Bertrand
MaRDI profile type: Publication
cites work: Q4740746
cites work: Q4095018
cites work: On the calculation of some differential Galois groups
cites work: Gauss Sums, Kloosterman Sums, and Monodromy Groups. (AM-116)
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description: scientific article; zbMATH DE number 4047842