On $\widehat{sl}(3)$ reduction, quantum gauge transformations, and ${\cal W}-$ algebras singular vectors

Details On $\widehat{sl}(3)$ reduction, quantum gauge transformations, and ${\cal W}-$ algebras singular vectors On $\widehat{sl}(3)$ reduction, quantum gauge transformations, and ${\cal W}-$ algebras singular vectors

1993-08-08

arxiv.org/abs/hep-th/9308038v2

Phys.Lett. B318 (1993) 85-91

Physics

High Energy Physics

High Energy Physics - Theory

9 pages

Scientific paper

10.1016/0370-2693(93)91788-O

The problem of describing the singular vectors of $\cW_3$ and $\cW_3^{(2)}$ Verma modules is addressed, viewing these algebras as BRST quantized Drinfeld-Sokolov (DS) reductions of $A^{(1)}_2\,$. Singular vectors of an $A^{(1)}_2\,$ Verma module are mapped into $\W$ algebra singular vectors and are shown to differ from the latter by terms trivial in the BRST cohomology. These maps are realized by quantum versions of the highest weight DS gauge transformations.

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