{"paper":{"title":"Braid groups of type ADE, Garside monoids, and the categorified root lattice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.RT"],"primary_cat":"math.QA","authors_text":"Anthony M. Licata, Hoel Queffelec","submitted_at":"2017-03-17T13:44:12Z","abstract_excerpt":"We study Artin-Tits braid groups $\\mathbb{B}_W$ of type ADE via the action of $\\mathbb{B}_W$ on the homotopy category $\\mathcal{K}$ of graded projective zigzag modules (which categorifies the action of the Weyl group $W$ on the root lattice). Following Brav-Thomas, we define a metric on $\\mathbb{B}_W$ induced by the canonical $t$-structure on $\\mathcal{K}$, and prove that this metric on $\\mathbb{B}_W$ agrees with the word-length metric in the canonical generators of the standard positive monoid $\\mathbb{B}_W^+$ of the braid group. We also define, for each choice of a Coxeter element $c$ in $W$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.06011","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"}