Systems of parameters and holonomicity of A-hypergeometric systems
Christine Berkesch Zamaere, Stephen Griffeth, Ezra Miller · Pacific Journal of Mathematics · 2015
We give an elementary proof of holonomicity for A-hypergeometric systems, with no requirements on the behavior of their singularities, a result originally due to Adolphson (1994) after the regular singular case by Gelfand and Gelfand (1986).Our method yields a direct de novo proof that A-hypergeometric systems form holonomic families over their parameter spaces, as shown by Matusevich, Miller, and Walther (2005).Dedication.Every now and then Andrei Zelevinsky had occasion to write a short and in many ways elementary paper with deep consequences.Particularly close to our hearts are his paper on graded nilpotent classes [Zelevinsky 1985] and his paper with Gelfand and Graev on hypergeometric systems [Gelfand et al. 1987]; both of these had enormous impact on our mathematical careers.It is in that spirit that we dedicate to Andrei this elementary perspective on topics that he influenced substantially for many years.