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

6 Citations (Scopus)

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
Pages (from-to)	88-96
Number of pages	9
Journal	Experimental Mathematics
Volume	32
Issue number	1
Early online date	27 Jun 2020
DOIs	https://doi.org/10.1080/10586458.2020.1780516
Publication status	Published - 1 Mar 2023
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.",

keywords = "Algorithm, Strong approximation, Symplectic group, Zariski density",

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

note = "Funding Information: A. S. Detinko was supported by Marie Sk{\l}odowska-Curie Individual Fellowship grant H2020 MSCA-IF-2015, no. 704910 (EU Framework Programme for Research and Innovation). A. Hulpke was supported by National Science Foundation grant DMS-1720146. We thank Professor Martin Kassabov for his helpful advice. Many thanks are due also to our referees, whose comments led to improvements of the paper. We are grateful to Mathematisches Forschungsinstitut Oberwolfach and the Hausdorff Research Institute for Mathematics for hospitality and facilitation of our work during visits in 2018. Publisher Copyright: {\textcopyright} 2020 Taylor \& Francis Group, LLC.",

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doi = "10.1080/10586458.2020.1780516",

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AU - Flannery, D. L.

AU - Hulpke, A.

N1 - Funding Information: A. S. Detinko was supported by Marie Skłodowska-Curie Individual Fellowship grant H2020 MSCA-IF-2015, no. 704910 (EU Framework Programme for Research and Innovation). A. Hulpke was supported by National Science Foundation grant DMS-1720146. We thank Professor Martin Kassabov for his helpful advice. Many thanks are due also to our referees, whose comments led to improvements of the paper. We are grateful to Mathematisches Forschungsinstitut Oberwolfach and the Hausdorff Research Institute for Mathematics for hospitality and facilitation of our work during visits in 2018. Publisher Copyright: © 2020 Taylor & Francis Group, LLC.

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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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VL - 32

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JO - Experimental Mathematics

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Experimenting with Symplectic Hypergeometric Monodromy Groups

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