Experimenting with Symplectic Hypergeometric Monodromy Groups

A. S. Detinko; D. L. Flannery; A. Hulpke

doi:10.1080/10586458.2020.1780516

Experimenting with Symplectic Hypergeometric Monodromy Groups

A. S. Detinko, D. L. Flannery, A. Hulpke

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

Abstract

We present new computational results for symplectic monodromy groups of hypergeometric differential equations. In particular, we compute the arithmetic closure of each group, sometimes justifying arithmeticity. The results are obtained by extending our earlier algorithms for Zariski dense groups, based on the strong approximation and congruence subgroup properties.

Original language	English
Journal	Experimental Mathematics
Early online date	27 Jun 2020
DOIs	https://doi.org/10.1080/10586458.2020.1780516
Publication status	E-pub ahead of print - 27 Jun 2020
Externally published	Yes

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title = "Experimenting with Symplectic Hypergeometric Monodromy Groups",

abstract = "We present new computational results for symplectic monodromy groups of hypergeometric differential equations. In particular, we compute the arithmetic closure of each group, sometimes justifying arithmeticity. The results are obtained by extending our earlier algorithms for Zariski dense groups, based on the strong approximation and congruence subgroup properties.",

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author = "Detinko, {A. S.} and Flannery, {D. L.} and A. Hulpke",

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AU - Hulpke, A.

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N2 - We present new computational results for symplectic monodromy groups of hypergeometric differential equations. In particular, we compute the arithmetic closure of each group, sometimes justifying arithmeticity. The results are obtained by extending our earlier algorithms for Zariski dense groups, based on the strong approximation and congruence subgroup properties.

AB - We present new computational results for symplectic monodromy groups of hypergeometric differential equations. In particular, we compute the arithmetic closure of each group, sometimes justifying arithmeticity. The results are obtained by extending our earlier algorithms for Zariski dense groups, based on the strong approximation and congruence subgroup properties.

KW - Algorithm

KW - Strong approximation

KW - Symplectic group

KW - Zariski density

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