{"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"}