Appears in collection : Representations, Probability, and Beyond : A Journey into Anatoly Vershik’s World

We shall discuss several partial results of ongoing work in collaboration (with I. Gaiur \& D. Van Straten and with V. Buchstaber \& I. Gaiur) on interesting properties of multiplication kernels, which include the famous Sonine –Gegenbauer formulas, examples of polynomials for Buchstaber–Kontsevich discriminant locus given as addition laws for special 2-valued formal groups (Buchstaber–Novikov–Veselov) as well as a connection of N-Bessel kernel discriminant loci with N-vlaued multiplication laws given by Buchstaber-Rees polynomials.