{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:U6NJMAMCLXRK5BJZT4SMWUOGEB","short_pith_number":"pith:U6NJMAMC","schema_version":"1.0","canonical_sha256":"a79a9601825de2ae85399f24cb51c62074a0ce96a249b2f0171600b58251a264","source":{"kind":"arxiv","id":"2506.07727","version":2},"attestation_state":"computed","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2506.07727","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-06-09T13:11:18Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"8d544d72bc45783e431677bbd018e776577e36736aaf54f2424cccd964bb7af9","abstract_canon_sha256":"2b8bcd9de7ff702bfb193ffc6eb58be430781057d077148e67fb071744d65149"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:00:28.167914Z","signature_b64":"pLwW15ohXDwUs7V6tBJP8dDl+kH+TD1Tvv2HWOasZY2KPV567T7tl0mC1SBUD9X368kdPmFfdOO/5jZ8H9AxDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a79a9601825de2ae85399f24cb51c62074a0ce96a249b2f0171600b58251a264","last_reissued_at":"2026-07-05T12:00:28.167404Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:00:28.167404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2506.07727","created_at":"2026-07-05T12:00:28.167467+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.07727v2","created_at":"2026-07-05T12:00:28.167467+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.07727","created_at":"2026-07-05T12:00:28.167467+00:00"},{"alias_kind":"pith_short_12","alias_value":"U6NJMAMCLXRK","created_at":"2026-07-05T12:00:28.167467+00:00"},{"alias_kind":"pith_short_16","alias_value":"U6NJMAMCLXRK5BJZ","created_at":"2026-07-05T12:00:28.167467+00:00"},{"alias_kind":"pith_short_8","alias_value":"U6NJMAMC","created_at":"2026-07-05T12:00:28.167467+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/U6NJMAMCLXRK5BJZT4SMWUOGEB","json":"https://pith.science/pith/U6NJMAMCLXRK5BJZT4SMWUOGEB.json","graph_json":"https://pith.science/api/pith-number/U6NJMAMCLXRK5BJZT4SMWUOGEB/graph.json","events_json":"https://pith.science/api/pith-number/U6NJMAMCLXRK5BJZT4SMWUOGEB/events.json","paper":"https://pith.science/paper/U6NJMAMC"},"agent_actions":{"view_html":"https://pith.science/pith/U6NJMAMCLXRK5BJZT4SMWUOGEB","download_json":"https://pith.science/pith/U6NJMAMCLXRK5BJZT4SMWUOGEB.json","view_paper":"https://pith.science/paper/U6NJMAMC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.07727&json=true","fetch_graph":"https://pith.science/api/pith-number/U6NJMAMCLXRK5BJZT4SMWUOGEB/graph.json","fetch_events":"https://pith.science/api/pith-number/U6NJMAMCLXRK5BJZT4SMWUOGEB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/U6NJMAMCLXRK5BJZT4SMWUOGEB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/U6NJMAMCLXRK5BJZT4SMWUOGEB/action/storage_attestation","attest_author":"https://pith.science/pith/U6NJMAMCLXRK5BJZT4SMWUOGEB/action/author_attestation","sign_citation":"https://pith.science/pith/U6NJMAMCLXRK5BJZT4SMWUOGEB/action/citation_signature","submit_replication":"https://pith.science/pith/U6NJMAMCLXRK5BJZT4SMWUOGEB/action/replication_record"}},"created_at":"2026-07-05T12:00:28.167467+00:00","updated_at":"2026-07-05T12:00:28.167467+00:00"}