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It turns out that $\\mathcal U$ is isomorphic to the coset vertex algebra $\\frak{psl}(n|n) _1 / \\frak{sl}(n)_1$, $n \\ge 3$. We show that $V_{-1}(\\frak{sl}(n))$ admits pr"},"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":"1805.09771","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-05-24T16:45:46Z","cross_cats_sorted":[],"title_canon_sha256":"521afa2ddc9ef3968fbf0fafe3a7a65227597b1be36cc03697e0f026461bebd0","abstract_canon_sha256":"d66e337cf32bb0376d873ae07780969c0b2a18fd7f8ec0b2c9974081e0cef8ac"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:23.123531Z","signature_b64":"HoVY08FeVorYe2Cs67g3JUbF5a6BxBZ/OR7YyDyTTSU5s16ye6knITrInC7ugPP0hMPYZd2APW59tCh/7hFqAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8e00f7785ef48df3b84f511acd8a38940d9a598599c2358e3eb22460d8ab0be8","last_reissued_at":"2026-05-18T00:04:23.122772Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:23.122772Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On some vertex algebras related to $V_{-1}(\\frak{sl} (n) )$ and their characters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Antun Milas, Drazen Adamovic","submitted_at":"2018-05-24T16:45:46Z","abstract_excerpt":"We consider several vertex operator (super)algebras closely related to $V_{-1}(\\frak{sl} (n) )$, $n \\ge 3$ : (a) the parafermionic subalgebra $K(\\frak{sl}(n),-1)$ for which we completely describe its inner structure, (b) the vacuum algebra $\\Omega (V_{-1}(\\frak{sl} (n) ) )$, and (c) an infinite extension $\\mathcal U$ of $V_{-1}(\\frak{sl} (n) )$ constructed by combining certain irreducible ordinary modules with integral weights. It turns out that $\\mathcal U$ is isomorphic to the coset vertex algebra $\\frak{psl}(n|n) _1 / \\frak{sl}(n)_1$, $n \\ge 3$. 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