Automorphisms of Coxeter groups and Lusztig's conjectures for Hecke algebras with unequal parameters

Abstract

Let $(W,S)$ be a Coxeter system, let $G$ be a finite solvable group of automorphisms of $(W,S)$ and let $\phi$ be a weight function which is invariant under $G$. Let ${\phi }_G$ denote the weight function on $W^G$ obtained by restriction from $\phi$. The aim of this paper is to compare the $\mathbf{a}$-function, the set of Duflo involutions and the Kazhdan-Lusztig cells associated to $(W,\phi )$ and to $(W^G,{\phi }_G)$, provided that Lusztig's Conjectures hold.

11 pages, few misprints corrected