{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/a-cyclotomic-family-of-thin-hypergeometric","title":"A cyclotomic family of thin hypergeometric monodromy groups in ${Sp}_4(\\mathbb{R})$","arxiv_id":"2106.09181","date":"2021-06-17","proceeding":null,"authors":["Simion Filip","Charles Fougeron"],"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.","url_abs":"https://arxiv.org/abs/2106.09181v2","url_pdf":"https://arxiv.org/pdf/2106.09181v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"a-cyclotomic-family-of-thin-hypergeometric","repo_url":"https://gitlab.com/fougeroc/notebook-cyclotomic-family","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}