{"paper":{"title":"Monoidal Categories associated with Kac-Moody Open Richardson Varieties in Symmetric Type","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RT","authors_text":"Yingjin Bi","submitted_at":"2026-04-24T02:57:01Z","abstract_excerpt":"In the present paper, we study the factorization properties of the generalized minors \\( \\Delta(w_{\\leq k}\\Lambda,\\, v_{\\leq k}\\Lambda), \\) introduced by Fomin--Zelevinsky, in the coordinate rings of Kac--Moody open Richardson varieties. By analyzing their simple factors in the monoidal category $\\mathscr{C}_{w,v}$, we connect the cluster algebra structure of these varieties with the categorical framework developed by Kashiwara--Kim--Oh--Park.\n  In particular, we prove that cluster monomials in the coordinate ring of a Kac--Moody open Richardson variety correspond to isomorphism classes of sim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.05184","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/2606.05184/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"}