THE ALGEBRA OF CONJUGACY CLASSES OF THE WREATH PRODUCT OF A FINITE GROUP WITH THE SYMMETRIC GROUP

Let G be a finite group. In this expository paper, we provide a detailed proof of the polynomiality property of the structure coefficients of the center of the wreath product G o S_n algebra. Our main tool is a universal combinatorial algebra which projects onto the center of the group G o S_n algebra for every n. We show that this universal algebra is isomorphic to the algebra of shifted symmetric functions on jG^?j alphabets.