Fusion rings for degenerate minimal models

Abstract

We study fusion rings for degenerate minimal models ($p=q$ case) for N=0 and N=1 (super)conformal algebras. We consider a distinguished family of modules at the level $c=1$ and $c=3/2$ and show that the corresponding fusion rings are isomorphic to the representation rings for $\mathfrak{s}l(2,\mathbf{C})$ and $\mathfrak{o}sp(1|2)$ respectively.

Revised and enlarged version. It includes all the results from math.QA/0101165 (to appear in Journal of Algebra)