Resonance equals reducibility for A-hypergeometric systems

Schulze, Mathias; Walther, Uli

doi:10.2140/ant.2012.6.527

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Resonance equals reducibility for $A$-hypergeometric systems

Mathias Schulze and Uli Walther

Vol. 6 (2012), No. 3, 527–537

DOI: 10.2140/ant.2012.6.527

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.

Keywords

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

Mathematical Subject Classification 2010

Primary: 13N10

Secondary: 32S40, 14M25

Milestones

Received: 1 October 2010

Revised: 4 January 2011

Accepted: 22 February 2011

Published: 5 July 2012

Authors

Mathias Schulze
Department of Mathematics Oklahoma State University Stillwater, OK 74078 United States

Uli Walther
Department of Mathematics Purdue University 150 North University Street West Lafayette, IN 47907-2067 United States

Vol. 6, No. 3, 2012