Remarks on the structure constants of the Verlinde algebra associated to $sl_3$

Abstract

The structure constants $N_{λ, μ}^{μ+ν}$ of the $sl_2$ Verlinde algebra as functions of $μ$ either vanish or can be expressed after a change of variable as the weight function of an irreducible representation of $sl_2$. We give a similar formula in the $sl_3$ case.