{"paper":{"title":"Representation theory of the vertex algebra $W_{1 + \\infty}$","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Andrey Radul (Howard University), Victor Kac (MIT)","submitted_at":"1995-12-18T21:13:03Z","abstract_excerpt":"In our paper~\\cite{KR} we began a systematic study of representations of the universal central extension $\\widehat{\\Cal D}\\/$ of the Lie algebra of differential operators on the circle. This study was continued in the paper~\\cite{FKRW} in the framework of vertex algebra theory. It was shown that the associated to $\\widehat {\\Cal D}\\/$ simple vertex algebra $W_{1+ \\infty, N}\\/$ with positive integral central charge $N\\/$ is isomorphic to the classical vertex algebra $W (gl_N)$, which led to a classification of modules over $W_{1 + \\infty, N}$. In the present paper we study the remaining non-tri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9512150","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/hep-th/9512150/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"}