Irreducible characters of the generalized symmetric group

Abstract

The paper studies how to compute irreducible characters of the generalized symmetric group $C_k\wr{S}_n$ by iterative algorithms. After reproving the Murnaghan-Nakayama rule by vertex algebraic method, we formulate a new iterative formula for characters of the generalized symmetric group. As applications, we find a numerical relation between the character values of $C_k\wr S_n$ and modular characters of $S_{kn}$.