{"paper":{"title":"Construction of PBW and canonical bases in the folding extension algebras for symmetrizable types","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Yumeng Wu","submitted_at":"2026-07-28T09:32:52Z","abstract_excerpt":"We study extension algebras arising from Lusztig's construction of perverse sheaves on quiver representation spaces equipped with an admissible automorphism $a$, leading to folding Khovanov--Lauda--Rouquier (KLR) algebras. Extending the method of M. Varagnolo and E. Vasserot to Lusztig's symmetrizable setting, we construct the skew group algebra $R(\\nu)\\langle\\mathbf{a}\\rangle$, where $\\mathbf{a}$ is induced by the admissible automorphism $a$, and show that $\\Ext^{\\bullet}(\\ ,L)$ preserves the signed basis and the crystal structure. In this framework, for finite types, we define standard and d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.25495","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/2607.25495/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"}