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 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 is not diagonalisable among the singular vectors.
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