{"paper":{"title":"Some extension algebras for standard modules over KLR algebras of type $A$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Alexander Kleshchev, David J. Steinberg, Doeke Buursma","submitted_at":"2019-06-26T23:12:14Z","abstract_excerpt":"Khovanov-Lauda-Rouquier algebras $R_\\theta$ of finite Lie type are affine quasihereditary with standard modules $\\Delta(\\pi)$ labeled by Kostant partitions of $\\theta$. Let $\\Delta$ be the direct sum of all standard modules. It is known that the Yoneda algebra $\\mathcal{E}_\\theta:=\\operatorname{Ext}_{R_\\theta}^*(\\Delta, \\Delta)$ carries a structure of an $A_\\infty$-algebra which can be used to reconstruct the category of standardly filtered $R_\\theta$-modules. In this paper, we explicitly describe $\\mathcal{E}_\\theta$ in two special cases: (1) when $\\theta$ is a positive root in type $\\mathtt{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.11380","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":""},"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"}