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

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 $\left(\frac{N-3}{2N},\frac{N-1}{2N},\frac{N+1}{2N},\frac{N+3}{2N}\right)$ at infinity and maximal unipotent monodromy at zero, for any integer $N\ge 4$. 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.

53 pages, 12 figures

Cited by in corpus (1)

• Cones and ping-pong in three dimensions