A cyclotomic family of thin hypergeometric monodromy groups in ${Sp}_4(\mathbb{R})$

Simion Filip; Charles Fougeron

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arXiv · 2106.09181

A cyclotomic family of thin hypergeometric monodromy groups in ${Sp}_4(\mathbb{R})$

Simion Filip·Charles Fougeron

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Abstract

We exhibit an infinite family of discrete subgroups of ${Sp}_4(\mathbb R)$ which have a number of remarkable properties. Our results are established by showing that each group plays ping-pong on an appropriate set of cones. The groups arise as the monodromy of hypergeometric differential equations with parameters $\left(\tfrac{N-3}{2N},\tfrac{N-1}{2N}, \tfrac{N+1}{2N}, \tfrac{N+3}{2N}\right)$ at infinity and maximal unipotent monodromy at zero, for any integer $N\geq 4$. Additionally, we relate the cones used for ping-pong in $\mathbb R^4$ with crooked surfaces, which we then use to exhibit domains of discontinuity for the monodromy groups in the Lagrangian Grassmannian.

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BibTeX RIS

Simion Filip, Charles Fougeron. 2021-06-17. A cyclotomic family of thin hypergeometric monodromy groups in ${Sp}_4(\mathbb{R})$. https://arxiv.org/abs/2106.09181

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