Kazhdan-Lusztig cells in some weighted Coxeter groups

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）.