English

Singular vectors of the $WA_2$ algebra

High Energy Physics - Theory 2009-10-28 v1

Abstract

The null vectors of an arbitrary highest weight representation of the WA2WA_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 W0W_0 is not diagonalisable among the singular vectors.

Keywords

Cite

@article{arxiv.hep-th/9403032,
  title  = {Singular vectors of the $WA_2$ algebra},
  author = {Z. Bajnok},
  journal= {arXiv preprint arXiv:hep-th/9403032},
  year   = {2009}
}

Comments

10 pages, LaTeX with 3 figures in LaTeX