{"paper":{"title":"Cells in Coxeter groups I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.GR"],"primary_cat":"math.RT","authors_text":"Mikhail V. Belolipetsky, Paul E. Gunnells","submitted_at":"2010-12-02T16:49:52Z","abstract_excerpt":"The purpose of this article is to shed new light on the combinatorial structure of Kazhdan-Lusztig cells in infinite Coxeter groups $W$. Our main focus is the set $\\D$ of distinguished involutions in $W$, which was introduced by Lusztig in one of his first papers on cells in affine Weyl groups. We conjecture that the set $\\D$ has a simple recursive structure and can be enumerated algorithmically starting from the distinguished involutions of finite Coxeter groups. Moreover, to each element of $\\D$ we assign an explicitly defined set of equivalence relations on $W$ that altogether conjecturally"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.0489","kind":"arxiv","version":4},"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"}