{"paper":{"title":"Geometric realization of affine bases: the Kronecker quiver case","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Jie Xiao, Yumeng Wu","submitted_at":"2026-06-18T02:08:28Z","abstract_excerpt":"In this paper, we study the transition matrix between the PBW basis and the canonical basis for the negative part of the quantized enveloping algebra of the Kronecker quiver from a geometric viewpoint. Building on Lusztig's geometric construction of the canonical basis, we construct sheaf-complex realizations of PBW basis elements by means of flag sheaf complexes over the strata $X(\\alpha,m)$ of representation varieties. Our first goal is to give a geometric description of the simple constituents appearing in the restrictions of these flag sheaf complexes to the strata $X(\\alpha,m)$. This allo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.19708","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/2606.19708/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"}