Singular vectors of the $WA_2$ algebra

Details Singular vectors of the $WA_2$ algebra Singular vectors of the $WA_2$ algebra

1994-03-06

arxiv.org/abs/hep-th/9403032v1

Phys.Lett. B329 (1994) 225-232

Physics

High Energy Physics

High Energy Physics - Theory

10 pages, LaTeX with 3 figures in LaTeX

Scientific paper

10.1016/0370-2693(94)90765-X

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.

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