AUTOMORPHISMS OF COXETER GROUPS AND LUSZTIG'S CONJECTURES FOR HECKE ALGEBRAS WITH UNEQUAL PARAMETERS

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 a-function, the set of Duflo involutions and the Kazhdan-Lusztig cells associated with (W, phi) and to (W-G, phi(G)), provided that Lusztig's Conjectures hold.