{"paper":{"title":"Construction of Irreducible Representations over Khovanov-Lauda-Rouquier Algebras of Finite Classical Type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Euiyong Park, Georgia Benkart, Se-Jin Oh, Seok-Jin Kang","submitted_at":"2011-08-04T11:20:05Z","abstract_excerpt":"We give an explicit construction of irreducible modules over Khovanov-Lauda-Rouquier algebras $R$ and their cyclotomic quotients $R^{\\lambda}$ for finite classical types using a crystal basis theoretic approach. More precisely, for each element $v$ of the crystal $B(\\infty)$ (resp. $B(\\lambda)$), we first construct certain modules $\\nabla(\\mathbf{a};k)$ labeled by the adapted string $\\mathbf{a}$ of $v$. We then prove that the head of the induced module $\\ind \\big(\\nabla(\\mathbf{a};1) \\boxtimes...\\boxtimes \\nabla(\\mathbf{a};n)\\big)$ is irreducible and that every irreducible $R$-module (resp. $R"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.1048","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"}