Differential Galois groups of confluent generalized hypergeometric equations: an approach using Stokes multipliers

Claudine Mitschi

Vol. 176 (1996), No. 2, 365–405

DOI: 10.2140/pjm.1996.176.365

Abstract

We explicitly compute the differential Galois groups of some families of generalized confluent hypergeometric equations by a method based on the asymptotic analysis of their irregular singularity at infinity. We obtain the Galois group directly from a particular set of topological generators. These are formal and analytic invariants of the equation, reflecting the asymptotic behaviour of the solutions. Our calculations yield classical groups as well as as the exceptional group G₂.

Mathematical Subject Classification 2000

Primary: 12H05

Secondary: 33C20

Milestones

Received: 18 October 1994

Published: 1 December 1996