{"paper":{"title":"Ordering Lusztig's families in type $B_n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Lacrimioara Iancu, Meinolf Geck","submitted_at":"2012-05-16T19:03:13Z","abstract_excerpt":"Let $W$ be a finite Coxeter group and $L$ be a weight function on $W$ in the sense of Lusztig. We have recently introduced a pre-order relation $\\preceq_L$ on the set of irreducible characters of $W$ which extends Lusztig's definition of \"families\" and which, conjecturally, corresponds to the ordering given by Kazhdan--Lusztig cells. Here, we give an explicit description of $\\preceq_L$ for $W$ of type $B_n$ and any $L$. (All other cases are known from previous work.) This crucially relies on some new combinatorial constructions around Lusztig's \"symbols\". Combined with previous work, we deduce"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.3762","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"}