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For any $k$-tuple $\\bm{\\lambda}=({\\lambda}_1, \\cdots, {\\lambda}_k)$ of weights of $\\fg$, and $k$-tuple $\\bm{a}=(a_1,\\cdots, a_k)$ of distinct non-zero complex numbers, we construct a class of modules $\\wt V(\\bm{\\lambda},\\bm{a})$ for the extended affine Lie algebra $\\wt\\fg(\\mu)$. We prove that the $\\wt\\fg(\\mu)$-module $\\wt V(\\bm{\\lambda},\\bm{a})$ is completely reducible. We also prove that the $\\wt\\fg(\\mu)$-module $\\wt V(\\b"},"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":"1711.01887","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-11-06T13:42:50Z","cross_cats_sorted":[],"title_canon_sha256":"936eb43a67a50e68a91afba9b19aedd55dfd05ebe547693ec362d77bf021ba86","abstract_canon_sha256":"462d47b8a79f8583d874f9eac3b198633f279f7fceb5bd53576dc6db2b645924"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:16.624632Z","signature_b64":"4jdz4BLxVXdeDXqaRzqwBtfWpG3XSQwjssrFayziISa3nNxd/DriakcDm+5dGMy5rKrEDOMYStZ6/3Ky8CqHDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"88e4d47a0a20186acac8b94a639b2713e99da6d6f48ff8e7c59e4cff07e3ff72","last_reissued_at":"2026-05-18T00:31:16.624240Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:16.624240Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Integrable representations for toroidal extended affine Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Fulin Chen, Shaobin Tan, Zhiqiang Li","submitted_at":"2017-11-06T13:42:50Z","abstract_excerpt":"Let $\\fg$ be any untwisted affine Kac-Moody algebra, $\\mu$ any fixed complex number, and $\\wt\\fg(\\mu)$ the corresponding toroidal extended affine Lie algebra of nullity two. For any $k$-tuple $\\bm{\\lambda}=({\\lambda}_1, \\cdots, {\\lambda}_k)$ of weights of $\\fg$, and $k$-tuple $\\bm{a}=(a_1,\\cdots, a_k)$ of distinct non-zero complex numbers, we construct a class of modules $\\wt V(\\bm{\\lambda},\\bm{a})$ for the extended affine Lie algebra $\\wt\\fg(\\mu)$. We prove that the $\\wt\\fg(\\mu)$-module $\\wt V(\\bm{\\lambda},\\bm{a})$ is completely reducible. 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