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 previous algorithms for Zariski dense groups, based on the strong approximation and congruence subgroup properties.

References in corpus (9)

• Mirror Symmetry and Integral Variations of Hodge Structure Underlying One Parameter Families of Calabi-Yau Threefolds
• Arithmeticity of Certain Symplectic Hypergeometric Groups
• Thin monodromy in Sp(4)
• Arithmeticity of Four Hypergeometric Monodromy Groups associated to Calabi-Yau threefolds
• Some monodromy groups of finite index in $S{p}_4(\mathbb{Z})$
• Zariski Density and Computing in Arithmetic Groups
• Algorithms for experimenting with Zariski dense subgroups
• The strong approximation theorem and computing with linear groups
• Constructive Membership Tests in Some Infinite Matrix Groups

Cited by in corpus (2)

• Symplectic Hypergeometric Groups of Degree Six
• Thin monodromy in $\mathrm{Sp}(4)$ and $\mathrm{Sp}(6)$