Resonance equals reducibility for A-hypergeometric systems

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.

9 pages, final version

References in corpus (2)

• Irregularity of hypergeometric systems via slopes along coordinate subspaces
• Hypergeometric D-modules and twisted Gauss-Manin systems

Cited by in corpus (10)

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• Monodromy of A-hypergeometric functions
• Algebraic aspects of hypergeometric differential equations
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• Euler--Mellin integrals and A-hypergeometric functions
• Confluent A-hypergeometric functions and rapid decay homology cycles
• The singular locus of Lauricella's F_C
• On the rank of an $A$-hypergeometric $D$-module versus the normalized volume of $A$
• Composition series for GKZ-systems
• Monodromies at infinity of confluent A-hypergeometric functions