Characters of Iwahori - Hecke Algebras

Iwahori-Hecke algebras for the innnite series of complex reeection groups G(r; p; n) were constructed recently in the work of Ariki and Koike, Brou e and Malle, and Ariki. In this paper we give Murnaghan-Nakayama type formulas for computing the irreducible characters of these algebras. Our method is a generalization of that in our earlier paper in which we derived Murnaghan-Nakayama rules for the characters of the Iwahori-Hecke algebras of the classical Weyl groups. In both papers we have been motivated by C. Greene, who gave a new derivation of the Murnaghan-Nakayama formula for irreducible symmetric group characters by summing diagonal matrix entries in Young's seminormal representations. We use the analogous representations of the Iwahori-Hecke algebra of G(r; p; n) given by Ariki.