We construct a commutative ring with identity which extends the ring of characters of finite dimensional representations of sl(3). It is generated by characters with values in the group ring $Z[\tilde{ W}]$ of the extended affine Weyl group of $\hat{ sl}(3)_k$ at $k\not \in Q$. The `quantised' version at rational level $k+3=3/p$ realises the fusion rules of a WZW conformal field theory based on admissible representations of $\hat{ sl}(3)_k$.
Categories: math.QA hep-th
