{"paper":{"title":"Realization of $U_q({\\mathfrak{sp}}_{2n})$ within the Differential Algebra on Quantum Symplectic Space","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.QA","math.SG"],"primary_cat":"math.RT","authors_text":"Jiao Zhang, Naihong Hu","submitted_at":"2016-09-17T02:06:13Z","abstract_excerpt":"We realize the Hopf algebra $U_q({\\mathfrak {sp}}_{2n})$ as an algebra of quantum differential operators on the quantum symplectic space $\\mathcal{X}(f_s;\\mathrm{R})$ and prove that $\\mathcal{X}(f_s;\\mathrm{R})$ is a $U_q({\\mathfrak{sp}}_{2n})$-module algebra whose irreducible summands are just its homogeneous subspaces. We give a coherence realization for all the positive root vectors under the actions of Lusztig's braid automorphisms of $U_q({\\mathfrak {sp}}_{2n})$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.05270","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"}