## Abstract

The Kac-Wakimoto admissible modules for ŝl_{2} are studied from the point of view of vertex operator algebras. It is shown that the vertex operator algebra L(l, 0) associated to irreducible highest weight modules at admissible level l = p/q - 2 is not rational if l is not a positive integer. However, a suitable change of the Virasoro algebra makes L(l, 0) a rational vertex operator algebra whose irreducible modules are exactly these admissible modules for ŝl_{2} and for which the fusion rules are calculated. It is also shown that the q-dimensions with respect to the new Virasoro algebra are modular functions.

Original language | English (US) |
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Pages (from-to) | 65-93 |

Number of pages | 29 |

Journal | Communications In Mathematical Physics |

Volume | 184 |

Issue number | 1 |

DOIs | |

State | Published - 1997 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

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