{"paper":{"title":"Orbifolds of symplectic fermion algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RT","authors_text":"Andrew R. Linshaw, Thomas Creutzig","submitted_at":"2014-04-10T04:20:08Z","abstract_excerpt":"We present a systematic study of the orbifolds of the rank $n$ symplectic fermion algebra $\\mathcal{A}(n)$, which has full automorphism group $Sp(2n)$. First, we show that $\\mathcal{A}(n)^{Sp(2n)}$ and $\\mathcal{A}(n)^{GL(n)}$ are $\\mathcal{W}$-algebras of type $\\mathcal{W}(2,4,\\dots, 2n)$ and $\\mathcal{W}(2,3,\\dots, 2n+1)$, respectively. Using these results, we find minimal strong finite generating sets for $\\mathcal{A}(mn)^{Sp(2n)}$ and $\\mathcal{A}(mn)^{GL(n)}$ for all $m,n\\geq 1$. We compute the characters of the irreducible representations of $\\mathcal{A}(mn)^{Sp(2n)\\times SO(m)}$ and $\\m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.2686","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1404.2686/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"}