Stokes matrices for confluent hypergeometric equations

Abstract

We apply the method of [arXiv:1705.07610] to compute the Stokes matrices of non-resonant confluent hypergeometric differential equations. We discuss the ambiguity of the presentation of the Stokes matrices regarding different choices. The results rely on an explicit description of the perverse sheaf associated to the non-confluent regular singular hypergeometric system arising via Fourier-Laplace transform. We give assumptions on the parameter such that the Stokes matrices have rational or real values. Under some more restrictive conditions, the Stokes matrices had been computed by Duval-Mitschi before. We compare our results with their formulae in the unramified case.

34 pages, 5 figures v4: section on the ramified case added, will be published in International Mathematics Research Notices

References in corpus (4)

• Isomonodromy Deformations at an Irregular Singularity with Coalescing Eigenvalues
• Local Fourier transforms and rigidity for D-modules
• Topological computation of some Stokes phenomena on the affine line
• Irregular Hodge filtration of some confluent hypergeometric systems

Cited by in corpus (2)

• Stokes matrices for Airy equations
• Remarks on rigid irreducible meromorphic connections on the projective line