{"paper":{"title":"Asymptotic lowest two-sided cell","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RT","authors_text":"C\\'edric Bonnaf\\'e (I3M), J\\'er\\'emie Guilhot","submitted_at":"2011-03-21T14:18:21Z","abstract_excerpt":"To a Coxeter system $(W,S)$ (with $S$ finite) and a weight function $L : W \\to \\NM$ is associated a partition of $W$ into Kazhdan-Lusztig (left, right or two-sided) $L$-cells. Let $S^\\circ = \\{s \\in S | L(s)=0\\}$, $S^+=\\{s \\in S | L(s) > 0\\}$ and let $C$ be a Kazhdan-Lusztig (left, right or two-sided) $L$-cell. According to the semicontinuity conjecture of the first author, there should exist a positive natural number $m$ such that, for any weight function $L' : W \\to \\NM$ such that $L(s^+)=L'(s^+) > m L'(s^\\circ)$ for all $s^+ \\in S^+$ and $s^\\circ \\in S^\\circ$, $C$ is a union of Kazhdan-Lusz"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.4025","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"}