{"paper":{"title":"Low-dimensional representations of the three component loop braid group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Eric C. Rowell, Julia Yael Plavnik, Liang Chang, Michael Yuan Sun, Paul Bruillard, Seung-Moon Hong","submitted_at":"2015-07-31T20:02:20Z","abstract_excerpt":"Motivated by physical and topological applications, we study representations of the group $\\mathcal{LB}_3$ of motions of $3$ unlinked oriented circles in $\\mathbb{R}^3$. Our point of view is to regard the three strand braid group $\\mathcal{B}_3$ as a subgroup of $\\mathcal{LB}_3$ and study the problem of extending $\\mathcal{B}_3$ representations. We introduce the notion of a \\emph{standard extension} and characterize $\\mathcal{B}_3$ representations admiting such an extension. In particular we show, using a classification result of Tuba and Wenzl, that every irreducible $\\mathcal{B}_3$ represent"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00005","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"}