A system of hypergeometric differential equations in two variables of rank 9

TL;DR

This paper investigates a rank 9 hypergeometric differential system in two variables, providing explicit solutions and monodromy data, advancing understanding of its structure and properties.

Contribution

It introduces a specific hypergeometric system of rank 9, constructs its fundamental solutions, and computes the circuit matrices for monodromy analysis.

Findings

Fundamental solutions expressed via hypergeometric series

Explicit circuit matrices for monodromy representation

Characterization of the system's singular locus and regular holonomicity

Abstract

We study a hypergeometric function in two variables and a system of hypergeometric differential equations associated with this function. This is a regular holonomic system of rank $9$. We give a fundamental system of solutions to this system in terms of this hypergeometric series. We give circuit matrices along generators of the fundamental group of the complement of its singular locus with respect to our fundamental system.