Generating functions for monomial characters of wreath products $\mathbb Z/d \mathbb Z \wr \mathfrak S_n$

Abstract

Let Z/dZ≀S n denote the wreath product of the cyclic group Z/dZ with the symmetric group S n . We define generating functions for monomial (induced one-dimensional) characters of Z/dZ≀S n and express these in terms of determinants and permanents. This extends work of Littlewood (The Theory of Group Characters and Representations of Groups, 1940) and Merris and Watkins (Linear Algebra Appl., 64, 1985) on generating functions for the monomial characters of S n .