Abstract
Following Lusztig, we consider a Coxeter group W together with a weight function L. This gives rise to the pre-order relation ⩽ L and the corresponding partition of W into left cells. We introduce an equivalence relation on weight functions such that, in particular, ⩽ 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.
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