Computing Kazhdan-Lusztig cells for unequal parameters

Following Lusztig, we consider a Coxeter group W together with a weight function L. This gives rise to the pre-order relation less than or equal to(L) and the corresponding partition of W into left cells. We introduce an equivalence relation on weight functions such that, in particular, less than or equal to(L) is constant on equivalent classes. We shall work this out explicitly for W of type F-4 and check that several of Lusztig's conjectures concerning left cells with unequal parameters hold in this case, even for those parameters which do not admit a geometric interpretation. The proofs involve some explicit computations using CHEVIE. (C) 2004 Elsevier Inc. All rights reserved.