Thin monodromy in $\mathrm{Sp}(4)$ and $\mathrm{Sp}(6)$
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| Format: | Preprint |
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2021
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| author | Bajpai, Jitendra Dona, Daniele Nitsche, Martin |
| author_facet | Bajpai, Jitendra Dona, Daniele Nitsche, Martin |
| contents | We explore the thinness of hypergeometric groups of type $\mathrm{Sp}(4)$ and $\mathrm{Sp}(6)$ by applying a new approach of computer-assisted ping pong. We prove the thinness of $17$ hypergeometric groups with maximally unipotent monodromy in $\mathrm{Sp}(6)$, 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 $\mathrm{Sp}(6)$, and of $3$ hypergeometric groups in $\mathrm{Sp}(4)$, completing the classification of all $\mathrm{Sp}(4)$ 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2112_12111 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Thin monodromy in $\mathrm{Sp}(4)$ and $\mathrm{Sp}(6)$ Bajpai, Jitendra Dona, Daniele Nitsche, Martin Group Theory 22E40, 32S40, 33C80 We explore the thinness of hypergeometric groups of type $\mathrm{Sp}(4)$ and $\mathrm{Sp}(6)$ by applying a new approach of computer-assisted ping pong. We prove the thinness of $17$ hypergeometric groups with maximally unipotent monodromy in $\mathrm{Sp}(6)$, 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 $\mathrm{Sp}(6)$, and of $3$ hypergeometric groups in $\mathrm{Sp}(4)$, completing the classification of all $\mathrm{Sp}(4)$ 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. |
| title | Thin monodromy in $\mathrm{Sp}(4)$ and $\mathrm{Sp}(6)$ |
| topic | Group Theory 22E40, 32S40, 33C80 |
| url | https://arxiv.org/abs/2112.12111 |