{"paper":{"title":"Schur-Weyl duality for certain infinite dimensional $\\rm{U}_q(\\mathfrak{sl}_2)$-modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Gus Lehrer, Kenji Iohara, Ruibin Zhang","submitted_at":"2018-11-04T05:51:20Z","abstract_excerpt":"Let $V$ be the two-dimensional simple module and $M$ be a projective Verma module for the quantum group of $\\mathfrak{sl}_2$ at generic $q$. We show that for any $r\\ge 1$, the endomorphism algebra of $M\\otimes V^{\\otimes r}$ is isomorphic to the type $B$ Temperley-Lieb algebra $\\rm{TLB}_r(q, Q)$ for an appropriate parameter $Q$ depending on $M$. The parameter $Q$ is determined explicitly. We also use the cellular structure to determine precisely for which values of $r$ the endomorphism algebra is semisimple. A key element of our method is to identify the algebras $\\rm{TLB}_r(q,Q)$ as the endom"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.01325","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"}