{"paper":{"title":"Quantized mixed tensor space and Schur-Weyl duality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RT","authors_text":"F. Stoll, R. Dipper, S. Doty","submitted_at":"2008-10-07T15:55:47Z","abstract_excerpt":"Let $R$ be a commutative ring with one and $q$ an invertible element of $R$. The (specialized) quantum group ${\\mathbf U} = U_q(\\mathfrak{gl}_n)$ over $R$ of the general linear group acts on mixed tensor space $V^{\\otimes r}\\otimes {V^*}^{\\otimes s}$ where $V$ denotes the natural $\\mathbf U$-module $R^n$, $r,s$ are nonnegative integers and $V^*$ is the dual $\\mathbf U$-module to $V$. The image of $\\mathbf U$ in $\\mathrm{End}_R(V^{\\otimes r}\\otimes {V^*}^{\\otimes s})$ is called the rational $q$-Schur algebra $S_{q}(n;r,s)$. We construct a bideterminant basis of $S_{q}(n;r,s)$. There is an actio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.1227","kind":"arxiv","version":4},"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"}