Fusion rules for admissible representations of affine algebras: the case of A2(1) Original Research Article

We describe the fusion rules for a series of admissible representations of sl(3) at fractional level 3/p − 3. Based on the analysis of some basic set of singular-vector decoupling equations we propose a formula for the fusion rule multiplicities generalising the Verlinde formula. The results admit an interpretation in terms of the affine Weyl group introduced by Kac and Wakimoto. It replaces the ordinary affine Weyl group in the analogous formula for the fusion rule multiplicities of integrable representations. Elements of the representation theory of a hidden finite-dimensional graded algebra behind the admissible representations are briefly discussed.