A note on decoupling conditions for generic level sl(3)k and fusion rules Original Research Article

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 w0·kΛ0. The result is a function with non-trivial singularities in the flag variables, namely a linear combination of 2F1 hypergeometric functions. This calculation fills in a gap in [Nucl. Phys. B 518 (1998) 645; Commun. Math. Phys. 202 (1999) 701]. and confirms the sl(3)k fusion rules determined there both for generic κ∉Q and fractional levels.