{"paper":{"title":"Irreducible Modules over Khovanov-Lauda-Rouquier Algebras of type $A_n$ and Semistandard Tableaux","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Euiyong Park, Seok-Jin Kang","submitted_at":"2010-05-09T09:14:33Z","abstract_excerpt":"Using combinatorics of Young tableaux, we give an explicit construction of irreducible graded modules over Khovanov-Lauda-Rouquier algebras $R$ and their cyclotomic quotients $R^{\\lambda}$ of type $A_{n}$. Our construction is compatible with crystal structure. Let ${\\mathbf B}(\\infty)$ and ${\\mathbf B}(\\lambda)$ be the $U_q(\\slm_{n+1})$-crystal consisting of marginally large tableaux and semistandard tableaux of shape $\\lambda$, respectively. On the other hand, let ${\\mathfrak B}(\\infty)$ and ${\\mathfrak B}(\\lambda)$ be the $U_q(\\slm_{n+1})$-crystals consisting of isomorphism classes of irredu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.1373","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":""},"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"}