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We show that the Schur functor $f_{rs}$ sends $M^{\\otimes s}$ to the $(F\\mathfrak{S}_{rs},F\\mathfrak{S}_s)$-bimodule $F\\mathfrak{S}_{rs} \\otimes_{F(\\mathfrak{S}_r \\wr \\mathfrak{S}_s)} ((f_rM)^{\\otimes s} \\otimes F\\mathfrak{S}_s)$. As a corollary, we obtain the effect of the Schur functor on the Lie power $L^s(M)$, symmetric power $S^s(M)$ and exte"},"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":"1102.4157","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2011-02-21T08:18:15Z","cross_cats_sorted":[],"title_canon_sha256":"924b95f99a7295a70bd320992f3232a0d63e7753e0b75f696e522a84efc18542","abstract_canon_sha256":"55e260ad98ad422519f7bbbf4029f6fc52a5377cf5e4183a361fbacb25a25344"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:27:56.267513Z","signature_b64":"yP5ELBQDF3NRTzeId4G1i33AQAyRI98HWmSyP0VODUyzYvQYjYO0lodlD+HZtxBZcaCZ9wvl5X+dq0oCD7k5Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e4a44b42145e4d41f8bd4f5cfed3934a509997c6eb38caf6096ce4e290928eb","last_reissued_at":"2026-05-18T04:27:56.267034Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:27:56.267034Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Schur functor on tensor powers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Kai Meng Tan, Kay Jin Lim","submitted_at":"2011-02-21T08:18:15Z","abstract_excerpt":"Let $M$ be a left module for the Schur algebra $S(n,r)$, and let $s \\in \\mathbb{Z}^+$. Then $M^{\\otimes s}$ is a $(S(n,rs), F\\mathfrak{S}_s)$-bimodule, where the symmetric group $\\mathfrak{S}_s$ on $s$ letters acts on the right by place permutations. We show that the Schur functor $f_{rs}$ sends $M^{\\otimes s}$ to the $(F\\mathfrak{S}_{rs},F\\mathfrak{S}_s)$-bimodule $F\\mathfrak{S}_{rs} \\otimes_{F(\\mathfrak{S}_r \\wr \\mathfrak{S}_s)} ((f_rM)^{\\otimes s} \\otimes F\\mathfrak{S}_s)$. As a corollary, we obtain the effect of the Schur functor on the Lie power $L^s(M)$, symmetric power $S^s(M)$ and exte"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4157","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":""},"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":"1102.4157","created_at":"2026-05-18T04:27:56.267106+00:00"},{"alias_kind":"arxiv_version","alias_value":"1102.4157v2","created_at":"2026-05-18T04:27:56.267106+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.4157","created_at":"2026-05-18T04:27:56.267106+00:00"},{"alias_kind":"pith_short_12","alias_value":"HZFEJNBBIXSN","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_16","alias_value":"HZFEJNBBIXSNIH4L","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_8","alias_value":"HZFEJNBB","created_at":"2026-05-18T12:26:30.835961+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/HZFEJNBBIXSNIH4L2T2473JZGS","json":"https://pith.science/pith/HZFEJNBBIXSNIH4L2T2473JZGS.json","graph_json":"https://pith.science/api/pith-number/HZFEJNBBIXSNIH4L2T2473JZGS/graph.json","events_json":"https://pith.science/api/pith-number/HZFEJNBBIXSNIH4L2T2473JZGS/events.json","paper":"https://pith.science/paper/HZFEJNBB"},"agent_actions":{"view_html":"https://pith.science/pith/HZFEJNBBIXSNIH4L2T2473JZGS","download_json":"https://pith.science/pith/HZFEJNBBIXSNIH4L2T2473JZGS.json","view_paper":"https://pith.science/paper/HZFEJNBB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1102.4157&json=true","fetch_graph":"https://pith.science/api/pith-number/HZFEJNBBIXSNIH4L2T2473JZGS/graph.json","fetch_events":"https://pith.science/api/pith-number/HZFEJNBBIXSNIH4L2T2473JZGS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HZFEJNBBIXSNIH4L2T2473JZGS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HZFEJNBBIXSNIH4L2T2473JZGS/action/storage_attestation","attest_author":"https://pith.science/pith/HZFEJNBBIXSNIH4L2T2473JZGS/action/author_attestation","sign_citation":"https://pith.science/pith/HZFEJNBBIXSNIH4L2T2473JZGS/action/citation_signature","submit_replication":"https://pith.science/pith/HZFEJNBBIXSNIH4L2T2473JZGS/action/replication_record"}},"created_at":"2026-05-18T04:27:56.267106+00:00","updated_at":"2026-05-18T04:27:56.267106+00:00"}