2003/12/20 by Meinolf Geck, Geck, Meinolf
Mathematics · #20C08 #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:20C08
paper · pdf · doi:10.48550/arxiv.math/0312392
arxiv created 2003/12/20 · arxiv updated 2009/12/01
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 F4 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 \sf CHEVIE.