{"paper":{"title":"Almost multiplicity-one property of spherical varieties over finite fields","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Fang Shi, Fulin Chen, Shaobin Tan","submitted_at":"2026-07-01T06:25:31Z","abstract_excerpt":"Let $H$ be a connected algebraic subgroup of a connected reductive group $G$ over a finite field $\\mathbb F_q$ such that $G/H$ is a $G$-spherical variety, i.e., $G/H$ has an open dense $B$-orbit for each Borel subgroup $B$ of $G$. We formulate, for the pair $(G,H)$, an almost multiplicity-one property. Then we establish a criterion for this property in terms of the $B$-stabilizers on $G/H$. In particular, we will see that this property is analogous to the strongly tempered condition in characteristic $0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.00496","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/2607.00496/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"}