Relating Jack wavefunctions to WA_(k-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 the WA_{k-1}(k+1,k+r) theory, we provide a proof for this conjecture.