Murnaghan-Nakayama rules for characters of Iwahori-Hecke algebras of classical type

Abstract

In this paper we give Murnaghan-Nakayama type formulas for computing the irreducible characters of the Iwahori-Hecke algebras of types A n − 1 , B n A_{n-1}, B_n , and D n D_n . Our method is a generalization of a derivation of the Murnaghan-Nakayama formula for the irreducible characters of the symmetric group given by Curtis Greene. Greene’s approach is to sum up the diagonal entries of the matrices of certain cycle permutations in Young’s seminormal representations. The analogues of the Young seminormal representations for the Iwahori-Hecke algebras of types A n − 1 , B n A_{n-1},B_n , and D n D_n were given by Hoefsmit.