Papers › A cyclotomic family of thin hypergeometric monodromy groups in Sp₄(ℝ)
A cyclotomic family of thin hypergeometric monodromy groups in Sp₄(ℝ)
Simion Filip, Charles Fougeron
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We exhibit an infinite family of discrete subgroups of Sp₄(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 (N-32N,N-12N, N+12N, N+32N) at infinity and maximal unipotent monodromy at zero, for any integer N≥4. Additionally, we relate the cones used for ping-pong in ℝ⁴ with crooked surfaces, which we then use to exhibit domains of discontinuity for the monodromy groups in the Lagrangian Grassmannian.
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