{"paper":{"title":"Lusztig sheaves and integrable highest weight modules in the symmetrizable case","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.QA","math.RA"],"primary_cat":"math.RT","authors_text":"Jie Xiao, Yixin Lan, Yumeng Wu","submitted_at":"2024-11-14T05:01:10Z","abstract_excerpt":"This paper continues the work of \\cite{fang2023lusztigsheavesintegrablehighest} and \\cite{fang2023lusztigsheavestensorproducts}. For a symmetrizable generalized Cartan matrix $C$ and the corresponding quantum group $\\mathbf{U}$, we consider an associated quiver $Q$ equipped with an admissible automorphism $a$. We construct a category $\\widetilde{\\mathcal{Q}/\\mathcal{N}}$ obtained from localizations of Lusztig sheaves for the corresponding framed and $2$-framed quivers with automorphism. The Grothendieck groups of these categories realize the integrable highest weight module $L(\\lambda)$ and th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.09188","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/2411.09188/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"}