{"paper":{"title":"On the representation theory of Virasoro Nets","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.OA","authors_text":"Sebastiano Carpi","submitted_at":"2003-06-30T12:37:28Z","abstract_excerpt":"We discuss various aspects of the representation theory of the local nets of von Neumann algebras on the circle associated with positive energy representations of the Virasoro algebra (Virasoro nets). In particular we classify the local extensions of the $c=1$ Virasoro net for which the restriction of the vacuum representation to the Virasoro subnet is a direct sum of irreducible subrepresentations with finite statistical dimension (local extensions of compact type). Moreover we prove that if the central charge $c$ is in a certain subset of $(1,\\infty)$, including $[2,\\infty)$, and $h \\geq (c-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0306425","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/math/0306425/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"}