Resonance equals reducibility for A-hypergeometric systems

TL;DR

This paper proves that A-hypergeometric systems are reducible if and only if their parameters are A-resonant, removing previous restrictions and simplifying the proof.

Contribution

It extends the characterization of reducibility in A-hypergeometric systems by removing confluence and Cohen-Macaulayness conditions, providing a more general result.

Findings

Reducibility corresponds exactly to A-resonance of parameters.

The proof is simplified and generalized beyond previous conditions.

The results unify and extend classical and recent theorems.

Abstract

Classical theorems of Gel'fand et al., and recent results of Beukers, show that non-confluent Cohen-Macaulay A-hypergeometric systems have reducible monodromy representation if and only if the continuous parameter is A-resonant. We remove both the confluence and Cohen-Macaulayness conditions while simplifying the proof.