### Abstract

We consider the quasihole wave functions 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 wave function. We find a duality between the differential equations fixing the electron and quasihole wave functions. They both satisfy the Laplace-Beltrami equation. We use this equation to obtain an analytic expression for the generic wave function with one excess flux. These results also apply to the more general models WA_{k-1} (k+1,k+r) corresponding to the recently introduced Jack states.

Original language | English (US) |
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Article number | 205307 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 82 |

Issue number | 20 |

DOIs | |

State | Published - Nov 8 2010 |

### All Science Journal Classification (ASJC) codes

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics

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## Cite this

*Physical Review B - Condensed Matter and Materials Physics*,

*82*(20), [205307]. https://doi.org/10.1103/PhysRevB.82.205307