{"paper":{"title":"Standard Monomials for Positroid Varieties","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AC","math.CO"],"primary_cat":"math.AG","authors_text":"Ayah Almousa, Daoji Huang, Shiliang Gao","submitted_at":"2023-09-27T03:31:14Z","abstract_excerpt":"We give an explicit characterization of the standard monomials for positroid varieties with respect to the Hodge degeneration and give a Gr\\\"obner basis. Furthermore, we show that promotion and evacuation biject standard monomials of a positroid variety with those of its cyclic shifts and $w_0$-reflection, respectively. The connection to promotion allows us to identify standard monomials of a positroid variety with Lam's cyclic Demazure crystal. Using a recurrence on the Hilbert series, we give an inductive formula for the character of cyclic Demazure modules."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.15384","kind":"arxiv","version":3},"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/2309.15384/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"}