{"paper":{"title":"Coordinate rings on symmetric spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG","math.QA"],"primary_cat":"math.RT","authors_text":"Huanchen Bao, Jinfeng Song","submitted_at":"2024-02-13T07:17:21Z","abstract_excerpt":"Let $G_k$ be a connected reductive group over an algebraically closed field $k$ of char $\\neq 2$. Let $\\theta_k$ be an algebraic group involution of $G_k$ and denote the fixed point subgroup by $K_k$. We construct an integral model for the symmetric space $K_k \\backslash G_k$ with a natural action of the Chevalley group scheme over integers. We show the coordinate ring $k[K_k \\backslash G_k]$ admits a canonical basis, as well as a good filtration as a $G_k$-module. We also construct a canonical basis and an integral form for the space of $K_k$-biinvariant functions on $k[G_k]$. Our results rel"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.08258","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/2402.08258/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"}