Fusion Rings Related to Affine Weyl Groups

Abstract

The construction of the fusion ring of a quasi-rational CFT based on $\widehat{sl}(3{)}_k$ at generic level $k\notin \mathbb{Q}$ is reviewed. It is a commutative ring generated by formal characters, elements in the group ring $\mathbb{Z}[\tilde{W}]$ of the extended affine Weyl group $\tilde{W}$ of $\widehat{sl}(3{)}_k$. Some partial results towards the $\widehat{sl}(4{)}_k$ generalisation of this character ring are presented.

13 pages; two figures. Talk at ``Lie Theory and Its Applications in Physics III'', Clausthal, 11-14 July, 1999, to appear in the Proceedings, eds. H.-D. Doebner et al