{"paper":{"title":"Braiding and asymptotic Schur's orthogonality","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.RT","authors_text":"A. Bendikov, A.Boyer, Ch. Pittet","submitted_at":"2023-07-10T13:04:58Z","abstract_excerpt":"Let $\\pi:G\\to U(\\mathcal H)$ be a unitary representation of a locally compact group. The braiding operator $F:\\mathcal H\\otimes\\mathcal H\\to \\mathcal H\\otimes\\mathcal H$, which flips the components of the Hilbert tensor product $F(v\\otimes w)=w\\otimes v$, belongs to the von Neumann algebra $W^*((\\pi\\otimes\\pi)(G\\times G))$ if and only if $\\pi$ is irreducible. Suppose $G$ is semisimple over a local field. If $G$ is non-compact with finite center, $P<G$ is a minimal parabolic, $\\pi:G\\to U(L^2(G/P))$ is the quasi-regular representation, then \\[\n  \\lim_{n\\to\\infty}\\frac{1}{\\int_{B_n}\\Xi(g)^2dg}\\in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.04538","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2307.04538/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"}