Algebra & Number Theory

Resonance equals reducibility for $A$-hypergeometric systems

Mathias Schulze and Uli Walther

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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.

Article information

Algebra Number Theory, Volume 6, Number 3 (2012), 527-537.

Received: 1 October 2010
Revised: 4 January 2011
Accepted: 22 February 2011
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 13N10: Rings of differential operators and their modules [See also 16S32, 32C38]
Secondary: 32S40: Monodromy; relations with differential equations and D-modules 14M25: Toric varieties, Newton polyhedra [See also 52B20]

toric hypergeometric Euler–Koszul $D$-module resonance monodromy


Schulze, Mathias; Walther, Uli. Resonance equals reducibility for $A$-hypergeometric systems. Algebra Number Theory 6 (2012), no. 3, 527--537. doi:10.2140/ant.2012.6.527.

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