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Due to Etingof--Kazhdan's construction, the level $c$ vacuum module $\\mathcal{V}_c(\\overline{R})$ for the algebra $\\textrm{A}(\\overline{R})$ possesses a quantum vertex algebra structure for any complex number $c$. We prove that any module for the quantum vertex algebra $\\mathcal{V}_c(\\overline{R})$ is naturally equipped with a structure of restricted $\\textrm{A}(\\overline{R})$-module of level"},"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":"1801.03543","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2018-01-10T20:20:54Z","cross_cats_sorted":["math-ph","math.MP","math.RT"],"title_canon_sha256":"83f2c0e212c3ad76f25ee35e273b5462bf55edb6fb03c4fa97cea5cff7b7e9f3","abstract_canon_sha256":"e0e78d1f532ee861470eb9f4ec1539f9d184a866c47428d0b2af4241b3c14b96"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:38.336279Z","signature_b64":"xFFydp5/hQjQXSlArvFAvPopeZcqcuICtQqprv3TnCz0CEYl0eqTjuB77W488InkZVxfj2RRsMlRp9qVjnITCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"59995d1178c67e0b9158d8264d3a78db025157cb25ef015b8a576ae9c5f02483","last_reissued_at":"2026-05-17T23:44:38.335897Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:38.335897Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantum current algebras associated with rational $R$-matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.RT"],"primary_cat":"math.QA","authors_text":"Slaven Ko\\v{z}i\\'c","submitted_at":"2018-01-10T20:20:54Z","abstract_excerpt":"We study quantum current algebra $\\textrm{A}(\\overline{R})$ associated with the rational $R$-matrix of $\\mathfrak{gl}_N$ and we give explicit formulae for the elements of its center at the critical level. 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