Arithmeticity of Certain Symplectic Hypergeometric Groups

TL;DR

This paper provides a criterion to determine when certain hypergeometric groups, arising from integral polynomials, are arithmetic subgroups of symplectic groups, enhancing understanding of their algebraic structure.

Contribution

It introduces a new sufficient condition linking integral polynomials to the arithmeticity of associated hypergeometric groups within symplectic groups.

Findings

Identifies specific conditions for arithmeticity of hypergeometric groups

Connects polynomial properties to group arithmeticity

Advances classification of symplectic hypergeometric groups

Abstract

We give a sufficient condition on a pair of (primitive) integral polynomials that the associated hypergeometric group (monodromy group of the corresponding hypergeometric differential equation) is an arithmetic subgroup of the integral symplectic group.