Torus equivariant D-modules and hypergeometric systems

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 Pi((A) over bar)(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 Pi((A) over bar)(B) to suitable binomial D-modules, we shed new light on the D-module theoretic properties of systems of classical hypergeometric differential equations. (C) 2019 Elsevier Inc. All rights reserved.