Relating Jack wavefunctions to WAk-1 theories

The (k, r) admissible Jack polynomials, recently proposed as many-body wavefunctions for non-Abelian fractional quantum Hall systems, have been conjectured to be related to some correlation functions of the minimal model WA(k-1)(k + 1, k + r) of the WA(k-1) algebra. By studying the degenerate representations of this conformal field theory, we provide a proof for this conjecture.