Thin monodromy in Sp(4) and Sp(6)

Bajpai, Jitendra and Dona, Daniele and Nitsche, Martin (2025) Thin monodromy in Sp(4) and Sp(6). JOURNAL OF ALGEBRA, 663. pp. 487-501. ISSN 0021-8693

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Abstract

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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