%0 Journal Article
%T Automorphisms of Coxeter groups and Lusztig's conjectures for Hecke algebras with unequal parameters
%A C¨¦dric Bonnaf¨¦
%J Mathematics
%D 2008
%I arXiv
%X Let $(W,S)$ be a Coxeter system, let $G$ be a finite solvable group of automorphisms of $(W,S)$ and let $\varphi$ be a weight function which is invariant under $G$. Let $\varphi_G$ denote the weight function on $W^G$ obtained by restriction from $\varphi$. The aim of this paper is to compare the ${\mathbf{a}}$-function, the set of Duflo involutions and the Kazhdan-Lusztig cells associated to $(W,\varphi)$ and to $(W^G,\varphi_G)$, provided that Lusztig's Conjectures hold.
%U http://arxiv.org/abs/0805.4269v3