{"paper":{"title":"Balanced tensor categories of representations of fixed-points conformal nets","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP","math.OA"],"primary_cat":"math.QA","authors_text":"Adri\\`a Mar\\'in-Salvador","submitted_at":"2026-06-04T17:08:04Z","abstract_excerpt":"Let $\\mathcal{A}$ be a (not necessarily rational) conformal net with a faithful action of a finite group $G$. Let $\\text{Rep}^G(\\mathcal{A})$ be the $G$-crossed balanced $\\mathrm{W}^*$-tensor category of $G$-twisted representations of $\\mathcal{A}$ as introduced in arXiv:2606.03623. We show that there is an equivalence of balanced $\\mathrm{W}^*$-tensor categories $(\\text{Rep}^G(\\mathcal{A}))^G\\cong \\text{Rep}(\\mathcal{A}^G)$ between the $G$-equivariantization of $\\text{Rep}^G(\\mathcal{A})$ and the category of representations of the fixed-points conformal net $\\mathcal{A}^G$. This generalizes t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06402","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/2606.06402/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"}