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We prove that for a particular value of $x$, the algebra $\\M_k(x)$ is the centralizer algebra of $\\uqsl$ acting on the $k$-fold tensor power of the sum of the 1-dimensional and 2-dimensional irreducible $\\uqsl$-modules. We show that $\\M_k(x)$ is generated by special diagrams $\\ell_i, t_i, r_i \\ (1 \\le i < k)$ and $p_j "},"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":"1106.5277","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-06-26T22:33:51Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"3b66c3725b6d6259a4422d506b7fe9c6d77f7aa9e3da23d819ca47fb63d11726","abstract_canon_sha256":"9696000e62003b4c11c83670480f5c6742a0756319de801921f913e8438643fa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:35.840270Z","signature_b64":"eQZSMGIjgLfdDm3nhpjIys5As54jZDlCqv051H9rrLgdhBCcw3ODqPdY9P6TkfiebIeg82Dc3pgstRfpJ16sAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ceb08e7b94fa595a58f089b66c90fdac1faf6436dabfe6fd5c413bf09b9ed0e2","last_reissued_at":"2026-05-18T03:20:35.839486Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:35.839486Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Motzkin Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Georgia Benkart, Tom Halverson","submitted_at":"2011-06-26T22:33:51Z","abstract_excerpt":"We introduce an associative algebra $\\M_k(x)$ whose dimension is the $2k$-th Motzkin number. 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