Assume that G is a finite group of exponent m with k conjugacy classes of elements. The operators discussed here are concerned with the ring of class functions on G, defined to be the ring of complex-valued functions on G that are constant on conjugacy classes. This ring is made into a C-algebra by identifying c in C with the constant function that is c everywhere. In fact we will restrict ourselves to functions with values that are elements of cyclotomic fields.
Elements of the ring are represented by the k values (elements of some cyclotomic field Q(zeta_n)) on the classes.