{"paper":{"title":"From tensor category to Temperley-Lieb algebra representation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Paul Martin, Peter E. Finch, Zoltan Kadar","submitted_at":"2016-07-29T19:44:12Z","abstract_excerpt":"We construct a representation of the Temperley-Lieb algebra from a multiplicity-free semisimple monoidal Abelian category ${\\cal C}$, with two simple objects $\\lambda$ and $\\nu$ such that $\\lambda\\otimes\\nu$ is simple and Hom$_{\\cal C}(\\lambda\\otimes \\lambda, \\nu)$ is not empty. A self-contained manual to tensor categories is also provided as well as a summary of the best known example of the construction: Schur-Weyl duality for $U_q(sl_2))$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.08908","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"}