Certifying Arithmeticity for Two Degree-Six Symplectic Hypergeometric Monodromy Groups
Group Theory
2026-05-26 v1 Representation Theory
Abstract
We prove arithmeticity for two degree-six symplectic hypergeometric monodromy groups, called C-47, and C-55 in the paper \cite{BajpaiDonaNitsche2025Thin} by Bajpai-Dona-Nitsche. This settles two of the three remaining cases, whose classification was left open by \cite{BajpaiDonaNitsche2025Thin}. The arithmeticity certificates were found with AlphaEvolve and then independently verified with exact matrix arithmetic over using a computer. We include illustrations of limit sets of several degree-six symplectic hypergeometric monodromy groups. Based on these illustration we conjecture C-32 to be thin.
Cite
@article{arxiv.2605.25935,
title = {Certifying Arithmeticity for Two Degree-Six Symplectic Hypergeometric Monodromy Groups},
author = {J. Maxwell Riestenberg and Diaaeldin Taha and Steve Trettel and Anna Wienhard},
journal= {arXiv preprint arXiv:2605.25935},
year = {2026}
}