{"paper":{"title":"On relative cuspidality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Nadir Matringe","submitted_at":"2025-06-10T02:59:30Z","abstract_excerpt":"Let $(\\mathbb{G},\\mathbb{H})$ be a symmetric pair of reductive groups over a $p$-adic field with $p\\neq 2$, attached to the involution $\\theta$. Under the assumption that there exists a maximally $\\theta$-split torus in $\\mathbb{G}$, which is anisotropic modulo its intersection with the split component of $\\mathbb{G}$, we extend Beuzart-Plessis' proof of existence of cuspidal representations, and prove that $\\mathbb{G}(F)$ admits strongly relatively cuspidal representations. This confirms expectations of Kato and Takano."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.08393","kind":"arxiv","version":2},"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/2506.08393/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"}