On the Monodromy Invariant Hermitian Form for $A$-Hypergeometric Systems

TL;DR

This paper constructs an explicit invariant Hermitian form for the monodromy of $A$-hypergeometric systems when a Mellin-Barnes basis exists, advancing understanding of their monodromy properties.

Contribution

It provides a new explicit construction of the monodromy invariant Hermitian form for $A$-hypergeometric systems with Mellin-Barnes bases.

Findings

Explicit Hermitian form construction for monodromy.

Conditions under which the form exists.

Enhanced understanding of monodromy invariants.

Abstract

We will give an explicit construction of the invariant Hermitian form for the monodromy of an $A$-hypergeometric system given that there is a Mellin-Barnes basis of solutions.