{"paper":{"title":"A new proof of the $\\mathfrak{sl}_{2}$ action on the triplet vertex algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.QA"],"primary_cat":"math.RT","authors_text":"Xianzu Lin","submitted_at":"2013-11-09T00:47:34Z","abstract_excerpt":"Let $\\mathcal {W}(p)$ be the triplet vertex algebra of central charge $c_{p}=1-\\frac{6(p-1)^{2}}{p}$, $p\\geq2$. As a Virasoro module, we have $$\\mathcal {W}(p)=\\bigoplus_{n=0} ^{\\infty}(2n+1) L(c_{p}, n^{2}p+np-n).$$ It was pointed out in \\cite{am1} that $\\mathcal {W}(p)$ admits an action of $\\mathfrak{sl}_{2}$. In this paper we give a combinatorics description of $\\mathcal {W}(p)$, from which the action of $\\mathfrak{sl}_{2}$ follows quite directly. In the end of this paper we give similar descriptions of the invariant subalgebra $\\mathcal {W}(p)^{\\Gamma}$, these will be useful for the charac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.2113","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}