# Stokes matrices for confluent hypergeometric equations

## TL;DR

This paper computes the Stokes matrices for confluent hypergeometric equations using a geometric approach, clarifies ambiguities, and compares results with previous work under specific conditions.

## Contribution

It provides an explicit method to determine Stokes matrices for confluent hypergeometric equations, including cases with rational or real values, and relates these to perverse sheaves and previous formulas.

## Key findings

- Explicit Stokes matrices for non-resonant confluent hypergeometric equations.
- Conditions for rational or real values of Stokes matrices.
- Comparison with Duval-Mitschi's formulas in the unramified case.

## 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.