Generalized centralizer rings of a finite group whose characters are the k-characters

Abstract

For a finite group [Formula: see text], the [Formula: see text]-characters are class function on subsets of [Formula: see text] called the [Formula: see text]-classes of [Formula: see text]. For a finite group [Formula: see text], the [Formula: see text]-class sums form a basis for a subring of [Formula: see text] which we call the [Formula: see text]-[Formula: see text]-ring of [Formula: see text], and we think of these rings as generalized centralizer rings. We show that [Formula: see text]-characters and extended [Formula: see text]-characters occur naturally as characters of the [Formula: see text]-[Formula: see text]-ring and that [Formula: see text]-characters occur naturally as characters of the [Formula: see text]-[Formula: see text]-ring.