A general framework for the polynomiality property of the structure coefficients of double-class algebras

In this paper, we build a general framework in which we give a formula that shows the form of the structure coefficients of double-class algebras and centers of group algebras. This formula allows us to give a polynomiality property for the structure coefficients of some important algebras. In particular, we re-obtain the polynomiality property of the structure coefficients in the cases of the center of the symmetric group algebra and the Hecke algebra of the pair (S_{2 n}, B_n). We also assign a new polynomiality property for the structure coefficients of the center of the hyperoctahedral group algebra and the Hecke algebra of the pair (Sn×Sn-1opp,diag(Sn-1)).