Let 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 algebra. Our main tool is a universal combinatorial algebra which projects onto the center of the group algebra for every . We show that this universal algebra is isomorphic to the algebra of shifted symmetric functions on alphabets.
"THE ALGEBRA OF CONJUGACY CLASSES OF THE WREATH PRODUCT OF A FINITE GROUP WITH THE SYMMETRIC GROUP." Rocky Mountain J. Math. 53 (2) 561 - 577, April 2023. https://doi.org/10.1216/rmj.2023.53.561