### Abstract

The null vectors of an arbitrary highest weight representation of the WA_{2} algebra are constructed. Using an extension of the enveloping algebra by allowing complex powers of one of the generators, analysed by Kent for the Virasoro theory, we generate all the singular vectors indicated by the Kac determinant. We prove that the singular vectors with given weights are unique up to normalisation and consider the case when W_{0} is not diagonalisable among the singular vectors.

Original language | English |
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Pages (from-to) | 225-232 |

Number of pages | 8 |

Journal | Physics Letters B |

Volume | 329 |

Issue number | 2-3 |

DOIs | |

Publication status | Published - Jun 16 1994 |

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

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## Cite this

Bajnok, Z. (1994). Singular vectors of the WA

_{2}algebra.*Physics Letters B*,*329*(2-3), 225-232. https://doi.org/10.1016/0370-2693(94)90765-X