Papers › Thin monodromy in Sp(4) and Sp(6)
Thin monodromy in Sp(4) and Sp(6)
Jitendra Bajpai, Daniele Dona, Martin Nitsche
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We explore the thinness of hypergeometric groups of type Sp(4) and Sp(6) by applying a new approach of computer-assisted ping pong. We prove the thinness of $17$ hypergeometric groups with maximally unipotent monodromy in Sp(6), completing the classification of all $40$ such groups into arithmetic and thin cases. In addition, we establish the thinness of further $46$ hypergeometric groups in Sp(6), and of $3$ hypergeometric groups in Sp(4), completing the classification of all Sp(4) hypergeometric groups. To the best of our knowledge, this article produces the first $63$ examples in the cyclotomic family of Zariski dense non-arithmetic hypergeometric monodromy groups of real rank three.
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