Vol. 6, No. 3, 2012

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ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Resonance equals reducibility for $A$-hypergeometric systems

Mathias Schulze and Uli Walther

Vol. 6 (2012), No. 3, 527–537

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.

toric, hypergeometric, Euler–Koszul, $D$-module, resonance, monodromy
Mathematical Subject Classification 2010
Primary: 13N10
Secondary: 32S40, 14M25
Received: 1 October 2010
Revised: 4 January 2011
Accepted: 22 February 2011
Published: 5 July 2012
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