{"paper":{"title":"ADE subalgebras of the triplet vertex algebra W(p): A-series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Antun Milas, Drazen Adamovic, Xianzu Lin","submitted_at":"2012-12-21T14:19:53Z","abstract_excerpt":"Motivated by \\cite{am1}, for every finite subgroup $\\Gamma \\subset PSL(2,\\mathbb{C})$ we investigate the fixed point subalgebra $\\triplet^{\\Gamma}$ of the triplet vertex $\\mathcal {W}(p)$, of central charge $1-\\frac{6(p-1)^{2}}{p}$, $p\\geq2$. This part deals with the $A$-series in the ADE classification of finite subgroups of $PSL(2,\\mathbb{C})$. First, we prove the $C_2$-cofiniteness of the $A_m$-fixed subalgebra $\\triplet^{A_m}$. Then we construct a family of $\\am$-modules, which are expected to form a complete set of irreps. As a strong support to our conjecture, we prove modular invariance"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.5453","kind":"arxiv","version":2},"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"}