{"paper":{"title":"Stable Centres I: Wreath Products","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GR","math.RA"],"primary_cat":"math.RT","authors_text":"Christopher Ryba","submitted_at":"2021-07-08T10:55:08Z","abstract_excerpt":"A result of Farahat and Higman shows that there is a ``universal'' algebra, $\\mathrm{FH}$, interpolating the centres of symmetric group algebras, $Z(\\mathbb{Z}S_n)$. We explain that this algebra is isomorphic to $\\mathcal{R} \\otimes \\Lambda$, where $\\mathcal{R}$ is the ring of integer-valued polynomials and $\\Lambda$ is the ring of symmetric functions. Moreover, the isomorphism is via ``evaluation at Jucys-Murphy elements'', which leads to character formulae for symmetric groups. Then, we generalise this result to wreath products $\\Gamma \\wr S_n$ of a fixed finite group $\\Gamma$. This involves"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2107.03752","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/2107.03752/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"}