{"paper":{"title":"Wreath Generalization of Littlewood Reciprocity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CO","authors_text":"Milo Bechtloff Weising","submitted_at":"2025-06-09T13:11:18Z","abstract_excerpt":"Given any $m$-dimensional complex representation $\\eta$ of a finite group $G$ and any highest weight representation $V^{\\lambda}$ of $\\mathrm{GL}_{nm}(\\mathbb{C})$ we may define an action of $G^n \\rtimes \\mathfrak{S}_n$ on $V^{\\lambda}$ using the embedding $\\mathrm{GL}_{m}(\\mathbb{C})^n \\rtimes \\mathfrak{S}_n \\leq \\mathrm{GL}_{nm}(\\mathbb{C})$ and $\\eta: G \\rightarrow \\mathrm{GL}_m(\\mathbb{C})$. We derive a branching rule for the multiplicities of irreducible $G^n \\rtimes \\mathfrak{S}_n$ representations in $V^{\\lambda}.$ The formula generalizes Littlewood's reciprocity rule for branching betwe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.07727","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/2506.07727/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"}