Monodromy of A-hypergeometric functions

TL;DR

This paper introduces a Mellin-Barnes integral method to compute a significant subgroup of the monodromy group of A-hypergeometric systems, potentially representing the entire monodromy group.

Contribution

It presents a novel integral-based approach to analyze the monodromy of A-hypergeometric functions, improving understanding of their monodromy groups.

Findings

Method computes a relevant subgroup of the monodromy group

Presumes this subgroup is the full monodromy group

Provides a major rewrite with improved insights

Abstract

Using Mellin-Barnes integrals we give a method to compute a relevant subgroup of the monodromy group of an A-hypergeometric system of differential equations. Presumably this group is the full monodromy group of the system. This article is a major rewrite of an article posted 2 years ago.