Kazhdan-Lusztig cells in some weighted Coxeter groups

• Published in: Science China. Mathematics Vol. 61; no. 2; pp. 325 - 352
• Main Authors: Shi, Jianyi, Yang, Gao
• Format: Journal Article
• Language: English
• Published: Beijing Science China Press 01.02.2018; Springer Nature B.V
• Subjects: Applications of Mathematics; Mathematics; Mathematics and Statistics; Weighting functions; 房间;加权;元素组成;iii;子区间; the second largest weight element; two-sided cells; universal elements; 20C08; left cells; weighted Coxeter group; 20F55
• ISSN: 1674-7283; 1869-1862
• DOI: 10.1007/s11425-017-9133-2

Let（W,S） be a Coxeter group with S = I■J such that J consists of all universal elements of S and that I generates a finite parabolic subgroup W_I of W with w_0 the longest element of W_I. We describe all the left cells and two-sided cells of the weighted Coxeter group（W,S,L） that have non-empty intersection with W_J,where the weight function L of（W, S） is in one of the following cases：（i） max{L（s） ｜ s ∈J} 〈 min{L（t）｜t∈I};（ii） min{L（s）｜s ∈J} ≥L（w_0）;（iii） there exists some t ∈ I satisfying L（t） 〈 L（s） for any s ∈I-{t} and L takes a constant value L_J on J with L_J in some subintervals of [1, L（w_0）-1]. The results in the case（iii） are obtained under a certain assumption on（W, W_I）.