Torus equivariant D-modules and hypergeometric systems

Christine Berkesch, Laura Felicia Matusevich, Uli Walther

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

We formalize, at the level of D-modules, the notion that A-hypergeometric systems are equivariant versions of the classical hypergeometric equations. For this purpose, we construct a functor Π B on a suitable category of torus equivariant D-modules and show that it preserves key properties, such as holonomicity, regularity, and reducibility of monodromy representation. We also examine its effect on solutions, characteristic varieties, and singular loci. By applying Π B to suitable binomial D-modules, we shed new light on the D-module theoretic properties of systems of classical hypergeometric differential equations.

Original languageEnglish (US)
Pages (from-to)1226-1266
Number of pages41
JournalAdvances in Mathematics
Volume350
DOIs
StatePublished - Jul 9 2019

Keywords

  • D-modules
  • GKZ
  • Horn system
  • Hypergeometric equations
  • Torus equivariant

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