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 A˜ 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 A˜ to suitable binomial D-modules, we shed new light on the D-module theoretic properties of systems of classical hypergeometric differential equations.
Original language | English (US) |
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Pages (from-to) | 1226-1266 |
Number of pages | 41 |
Journal | Advances in Mathematics |
Volume | 350 |
DOIs | |
State | Published - Jul 9 2019 |
Bibliographical note
Funding Information:CB was partially supported by NSF Grants DMS 1440537, OISE 0964985, DMS 0901123, and DMS 1661962.LFM was partially supported by NSF Grants DMS 0703866, DMS 1001763, and a Sloan Research Fellowship.UW was partially supported by NSF Grants DMS 0901123 and 1401392, and by Simons Collaboration Grant #580839.
Publisher Copyright:
© 2019 Elsevier Inc.
Keywords
- D-modules
- GKZ
- Horn system
- Hypergeometric equations
- Torus equivariant