{"paper":{"title":"A note on representations of some affine vertex algebras of type D","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Ozren Perse","submitted_at":"2012-05-14T12:35:32Z","abstract_excerpt":"In this note we construct a series of singular vectors in universal affine vertex operator algebras associated to $D_{\\ell}^{(1)}$ of levels $n-\\ell+1$, for $n \\in \\Z_{>0}$. For $n=1$, we study the representation theory of the quotient vertex operator algebra modulo the ideal generated by that singular vector. In the case $\\ell =4$, we show that the adjoint module is the unique irreducible ordinary module for simple vertex operator algebra $L_{D_{4}}(-2,0)$. We also show that the maximal ideal in associated universal affine vertex algebra is generated by three singular vectors."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.3003","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":""},"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"}