{"paper":{"title":"Some Non-Trivial Kazhdan-Lusztig Coefficients of an Affine Weyl Group of Type $\\tilde A_n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Leonard Scott, Nanhua XI","submitted_at":"2009-09-18T13:03:23Z","abstract_excerpt":"In this paper we show that the leading coefficient $\\mu(y,w)$ of some Kazhdan-Lusztig polynomials $P_{y,w}$ with $y,w$ in an affine Weyl group of type $\\tilde A_n $ is $n+2$. This fact has some consequences on the dimension of first extension groups of finite groups of Lie type with irreducible coefficients."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.3394","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"}