Classical theorems of Gel’fand et al. and recent results of Beukers show that nonconfluent Cohen–Macaulay -hypergeometric systems have reducible monodromy representation if and only if the continuous parameter is -resonant.
We remove both the confluence and Cohen–Macaulayness conditions while simplifying the proof.
"Resonance equals reducibility for $A$-hypergeometric systems." Algebra Number Theory 6 (3) 527 - 537, 2012. https://doi.org/10.2140/ant.2012.6.527