{"paper":{"title":"Universal characters twisted by roots of unity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Seamus P. Albion","submitted_at":"2022-12-14T17:11:45Z","abstract_excerpt":"A classical result of Littlewood gives a factorisation for the Schur function at a set of variables \"twisted\" by a primitive $t$-th root of unity, characterised by the core and quotient of the indexing partition. While somewhat neglected, it has proved to be an important tool in the character theory of the symmetric group, the cyclic sieving phenomenon, plethysms of symmetric functions and more. Recently, similar factorisations for the characters of the groups $\\mathrm{O}(2n,\\mathbb{C})$, $\\mathrm{Sp}(2n,\\mathbb{C})$ and $\\mathrm{SO}(2n+1,\\mathbb{C})$ were obtained by Ayyer and Kumari. We lift"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2212.07343","kind":"arxiv","version":3},"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/2212.07343/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"}