Singular Vectors of W Algebras via Ds Reduction of A
نویسندگان
چکیده
The BRST quantisation of the Drinfeld-Sokolov reduction applied to the case of A (1) 2 is explored to construct in an unified and systematic way the general singular vectors in W 3 and W (2) 3 Verma modules. The construction relies on the use of proper quantum analogues of the classical DS gauge fixing transformations. Furthermore the stability groups W (η) of the highest weights of the W-Verma modules play an important role in the proof of the BRST equivalence of the Malikov-Feigin-Fuks singular vectors and the W algebra ones. The resulting singular vectors are essentially classified by the affine Weyl group W modulo W (η) .
منابع مشابه
SISSA – 106/93/EP ON ̂ sl(3) REDUCTION, QUANTUM GAUGE TRANSFORMATIONS, AND W − ALGEBRAS SINGULAR VECTORS
The problem of describing the singular vectors of W 3 and W (2) 3 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 th...
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