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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1005.1373","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-05-09T09:14:33Z","cross_cats_sorted":[],"title_canon_sha256":"2d11a8b81bd176c47ccd2c97c21cc1c2a7b2cd48f14c7619852eef50eb483faa","abstract_canon_sha256":"af28a468d18e0bf6783071da77cfd9842b30020fc1bd72f9b15ee4d6be80635a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:42:14.515664Z","signature_b64":"ogOcChQSkvN1/MthFWpdV5qBYaa3oxfaeE2RhPK5B1iTFWlT15PfZQ4dXO19Ga31+eeHEJVSJ7dngifaFjH4DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3021b8da2d65e1baa301942af139d6ddb4ab3413f5231b966abdd9a47c9c46c7","last_reissued_at":"2026-05-18T04:42:14.515001Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:42:14.515001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $A_{n}$. 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