{"paper":{"title":"Representations of the Necklace Braid Group: Topological and Combinatorial Approaches","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Alex Bullivant, Andrew Kimball, Eric C. Rowell, Paul Martin","submitted_at":"2018-10-11T17:53:08Z","abstract_excerpt":"The necklace braid group $\\mathcal{NB}_n$ is the motion group of the $n+1$ component necklace link $\\mathcal{L}_n$ in Euclidean $\\mathbb{R}^3$. Here $\\mathcal{L}_n$ consists of $n$ pairwise unlinked Euclidean circles each linked to an auxiliary circle. Partially motivated by physical considerations, we study representations of the necklace braid group $\\mathcal{NB}_n$, especially those obtained as extensions of representations of the braid group $\\mathcal{B}_n$ and the loop braid group $\\mathcal{LB}_n$. We show that any irreducible $\\mathcal{B}_n$ representation extends to $\\mathcal{NB}_n$ in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.05152","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"}