{"paper":{"title":"High-dimensional representations of the 3-component loop braid group","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.RA","authors_text":"Lieven Le Bruyn","submitted_at":"2015-08-04T18:56:03Z","abstract_excerpt":"In a recent paper here arXiv:1508.0005 it is shown that irreducible representations of the three string braid group $B_3$ of dimensions $\\leq 5$ extend to representations of the 3-component loop braid group $LB_3$. Further, an explicit $6$-dimensional irreducible $B_3$-representation is given that does not extend. In this note we give a necessary and sufficient condition, in all dimensions, on the components of irreducible representations of the modular group $\\Gamma$ such that sufficiently general representations extend to $\\Gamma \\ast_{C_3} S_3$. As a consequence, the corresponding irreducib"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00871","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"}