We consider the quasihole wavefunctions of the non-abelian Read-Rezayi quantum Hall states which are given by the conformal blocks of the minimal model $WA_{k-1}(k+1, k+2)$ of the $WA_{k-1}$ algebra. By studying the degenerate representations of this conformal field theories, we derive a second order differential equation satisfied by a general many-quasihole wavefunction. We find a surprising duality between the differential equations fixing the electron and quasihole wavefunctions: they both satisfy a Calogero-Sutherland type equation. We use this equation to obtain an analytic expression for the generic wavefunction with one excess flux. This analysis also applies to the more general models $WA_{k-1}(k+1, k+r)$ corresponding to the recently introduced Jack states. These results hints at some novel structure about non polynomial solutions of Calogero-Sutherland Hamiltonian.

Amsterdam