Torus equivariant D-modules and hypergeometric systems

Christine Berkesch; Laura Felicia Matusevich; Uli Walther

doi:10.1016/j.aim.2019.04.050

Torus equivariant D-modules and hypergeometric systems

Christine Berkesch, Laura Felicia Matusevich, Uli Walther

Mathematics

Research output: Contribution to journal › Article › peer-review

4 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 ^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)
Pages (from-to)	1226-1266
Number of pages	41
Journal	Advances in Mathematics
Volume	350
DOIs	https://doi.org/10.1016/j.aim.2019.04.050
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

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title = "Torus equivariant D-modules and hypergeometric systems",

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.",

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AU - Berkesch, Christine

AU - Matusevich, Laura Felicia

AU - Walther, Uli

N1 - 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.

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N2 - 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.

AB - 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.

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KW - Horn system

KW - Hypergeometric equations

KW - Torus equivariant

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Torus equivariant D-modules and hypergeometric systems

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Bibliographical note

Keywords

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