{"paper":{"title":"On parafermion vertex algebras of $\\frak{sl}(2)_{-3/2}$ and $\\frak{sl}(3)_{-3/2}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.RT"],"primary_cat":"math.QA","authors_text":"Antun Milas, Drazen Adamovic, Qing Wang","submitted_at":"2020-05-06T07:32:10Z","abstract_excerpt":"We study parafermion vertex algebras $N_{-3/2}(\\frak{sl}(2))$ and $N_{-3/2}(\\frak{sl}(3))$. Using the isomorphism between $N_{-3/2}(\\frak{sl}(3))$ and the logarithmic vertex algebra $\\mathcal{W}^{0} (2)_{A_2} $ from [2], we show that these parafermion vertex algebras are infinite direct sums of irreducible modules for the Zamolodchikov algebra $\\mathcal{W}(2,3)$ of central charge $c=-10$, and that $N_{-3/2}(\\frak{sl}(3))$ is a direct sum of irreducible $N_{-3/2}(\\frak{sl}(2))$-modules. As a byproduct, we prove certain conjectures about the vertex algebra $\\mathcal{W}^0(p)_{A_2}$. We also obtai"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2005.02631","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2005.02631/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}