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We study a certain extension $V$ of a tensor product of finitely many copies of the orbifold model $V_{\\sqrt{2}A_{p-1}}^{\\langle \\widehat{\\sigma} \\rangle}$ and give a criterion for $V$ that every irreducible $V$-module is a simple current."},"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":"1708.06082","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2017-08-21T05:45:22Z","cross_cats_sorted":[],"title_canon_sha256":"285f9719e5302b613a5454669629b62d0ff894cbaf49d455785eb85cef9799e6","abstract_canon_sha256":"60a6a23fa7e50266ed84f26047ad4e81c0a793c7043a635c8692dd7ebfcf85bc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:37:43.298289Z","signature_b64":"OEv1Gia5lIC3+1MStuhMdeI4qXgWkzRK6QPnH9t1EwcnkCzfrC0VdgPOlyKUteCBRAx9Uj8gAP359oNloNCSDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"79b8ec222d3c2e8e4cc6fe9c5c27c5157c643ab12eabda6e6d4478c7c73427a7","last_reissued_at":"2026-05-18T00:37:43.297709Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:37:43.297709Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extensions of tensor products of ${\\mathbb Z}_p$-orbifold models of the lattice vertex operator algebra $V_{\\sqrt{2}A_{p-1}}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Ching Hung Lam, Hiromichi Yamada, Toshiyuki Abe","submitted_at":"2017-08-21T05:45:22Z","abstract_excerpt":"Let $p$ be an odd prime and let $\\widehat{\\sigma}$ be an order $p$ automorphism of $V_{\\sqrt{2}A_{p-1}}$ which is a lift of a $p$-cycle in the Weyl group ${\\rm Weyl}(A_{p-1})\\cong {\\mathfrak S}_p$. 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