The Grothendieck Ring of a Family of Spherical Categories

Abstract

We compute the fusion rule of a one-parameter family of spherical categories constructed by one author from the classification of singly generated Yang–Baxter planar algebras. The structure constant of the fusion rule is expressed in a closed-form formula of Littlewood–Richardson coefficients. We also compute the characters of the simple objects and their generating function in terms of symmetric functions with infinite variables.