{"paper":{"title":"Matching realization of $U_q(sl_{n+1})$ of higher rank in the quantum Weyl algebra $\\mathcal W_q(2n)$","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Naihong Hu, Shenyou Wang","submitted_at":"2014-01-31T14:56:20Z","abstract_excerpt":"In the paper, we further realize the higher rank quantized universal enveloping algebra $U_q(sl_{n+1})$ as certain quantum differential operators in $\\mathcal W_q(2n)$ defined over the quantum divided power algebra $\\mathcal{A}_q(n)$ of rank $n$. We give the quantum differential operators realization for both the simple root vectors and the non-simple root vectors of $U_q(sl_{n+1})$. The nice behavior of the quantum root vectors formulas under the action of the Lusztig symmetries once again indicates that our realization model is naturally matched."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.8184","kind":"arxiv","version":1},"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"}