A Note on Decoupling Conditions for Generic Level ŝl ( 3 ) k and Fusion Rules

We find the solution of the sl(3) k singular vector decoupling equations on 3–point functions for the particular case when one of the fields is of weight w 0 · kΛ 0. The result is a function with non-trivial singularities in the flag variables, namely a linear combination of 2 F 1 hypergeometric functions. This calculation fills in a gap in [1] and confirms the sl(3) k fusion rules determined there both for generic κ ∈ Q and fractional levels. We have also analysed the fusion in sl(3) k using algebraic methods generalising those of Feigin and Fuchs and again find agreement with [1]. In the process we clarify some details of previous treatments of the fusion of sl(2) k fractional level admissible representations.