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

TL;DR

This paper explores the structure constants of the $sl_3$ Verlinde algebra, providing a formula that relates these constants to the weight functions of irreducible $sl_3$ representations, extending known results from $sl_2$.

Contribution

It introduces a new formula for the structure constants of the $sl_3$ Verlinde algebra, generalizing the $sl_2$ case and linking them to representation weight functions.

Findings

The structure constants can be expressed as weight functions of $sl_3$ representations.

A formula analogous to the $sl_2$ case is established for $sl_3$.

The results deepen understanding of the algebraic structure of $sl_3$ Verlinde algebra.

Abstract

The structure constants $N_{\lambda, \mu}^{\mu+\nu}$ of the $sl_2$ Verlinde algebra as functions of $\mu$ 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.