{"paper":{"title":"Cells and cacti","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"C\\'edric Bonnaf\\'e (IMAG)","submitted_at":"2015-06-25T13:06:14Z","abstract_excerpt":"Let $(W,S)$ be a Coxeter system, let $\\varphi$ be a weight function on $S$ and let ${\\mathrm{Cact}}\\_W$ denote the associated {\\it cactus group}. Following an idea of I. Losev, we construct an action of ${\\mathrm{Cact}}\\_W  \\times {\\mathrm{Cact}}\\_W$ on $W$ which has nice properties with respect to the partition of $W$ into left, right or two-sided cells (under some hypothesis, which hold for instance if $\\varphi$ is constant or if $W$ is finite of rank $\\textless{} 5$). It must be noticed that the action depends heavily on $\\varphi$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.07737","kind":"arxiv","version":3},"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"}