Resonance equals reducibility for $A$-hypergeometric systems

Abstract

Classical theorems of Gel’fand et al. and recent results of Beukers show that nonconfluent 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.