{"paper":{"title":"Representations of $a_{\\infty}$ and $d_{\\infty}$ with central charge 1 on the single neutral fermion Fock space $\\mathit{F^{\\otimes \\frac{1}{2}}}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.QA","math.RT"],"primary_cat":"math-ph","authors_text":"Ben Cox, Elizabeth Jurisich, Iana I. Anguelova","submitted_at":"2013-09-28T18:24:15Z","abstract_excerpt":"We construct a new representation of the infinite rank Lie algebra $a_{\\infty}$ with central charge $c=1$ on the Fock space $\\mathit{F^{\\otimes \\frac{1}{2}}}$ of a single neutral fermion. We show that $\\mathit{F^{\\otimes \\frac{1}{2}}}$ is a direct sum of irreducible integrable highest weight modules for $a_{\\infty}$ with central charge $c=1$. We prove that as $a_{\\infty}$ modules $\\mathit{F^{\\otimes \\frac{1}{2}}}$ is isomorphic to the Fock space $\\mathit{F^{\\otimes 1}}$ of the charged free fermions. As a corollary we obtain the decompositions of certain irreducible highest weight modules for $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7487","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"}