Stokes matrices of hypergeometric integrals

TL;DR

This paper computes the Stokes matrices for hypergeometric integrals related to hyperplane arrangements, extending previous work on confluent hypergeometric functions, using explicit solutions and combinatorial methods.

Contribution

It generalizes the calculation of Stokes matrices to hypergeometric integrals associated with hyperplane arrangements in generic position.

Findings

Explicit formulas for Stokes matrices of hypergeometric integrals

Extension of previous confluent hypergeometric results

Use of combinatorial relations between integrals

Abstract

In this work we compute the Stokes matrices of the ordinary differential equation satisfied by the hypergeometric integrals associated to an arrangement of hyperplanes in generic position. This generalizes the computation done by Ramis and Duval for confluent hypergeometric functions, which correspond to the arrangement of two points on the line. The proof is based on an explicit description of a base of canonical solutions as integrals on the cones of the arrangement, and combinatorial relations between integrals on cones and on domains.