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Résumé |
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. |
