{"paper":{"title":"On the relative Langlands duality for $\\operatorname{Sp}_{2n} \\backslash \\operatorname{GL}_{2n+1}$ (with an appendix by Zeyu Wang)","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.RT","authors_text":"Guodong Xi, Weixiao Lu, Zeyu Wang","submitted_at":"2025-04-26T03:06:45Z","abstract_excerpt":"We verify the relative Langlands duality conjecture proposed by Ben-Zvi, Sakellaridis, Venkatesh for the hyperspherical Hamiltonian variety $T^*(\\operatorname{Sp}_{2n}\\backslash \\operatorname{GL}_{2n+1})$. We provide numerical (over number fields and function fields) and geometric (in the \\'{e}tale setting) evidence that its dual Hamiltonian variety should be $T^*(\\operatorname{GL}_n \\times \\operatorname{GL}_{n+1} \\backslash \\operatorname{GL}_{2n+1})$ as is predicted by Ben-Zvi, Sakellaridis, Venkatesh."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.18774","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.18774/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}