Virasoro Singular Vectors via Quantum DS Reduction

Abstract

The BRST quantisation of the Drinfeld - Sokolov reduction is exploited to recover all singular vectors of the Virasoro algebra Verma modules from the corresponding $A_1^{(1)}$ ones. The two types of singular vectors are shown to be identical modulo terms trivial in the $Q_{BRST}$ cohomology. The main tool is a quantum version of the DS gauge transformation.

7 pages, plain TeX, SISSA-74/93/EP

References in corpus (4)

• Solutions of the Knizhnik - Zamolodchikov Equation with Rational Isospins and the Reduction to the Minimal Models
• Singular Vectors of the Virasoro Algebra
• Reduction of the Knizhnik-Zamolodchikov Equation - a Way of Producing Virasoro Algebra Singular Vectors
• Fusion and singular vectors in A1{(1)} highest weight cyclic modules

Cited by in corpus (8)

• $A_1^{(1)}$ Admissible Representations -- Fusion Transformations and Local Correlators
• Hamiltonian Reduction of $SL(2)$-theories at the Level of Correlators
• Singular Vectors of $\mathcal{W}$ Algebras via DS Reduction of $A_2^{(}1)$
• Families of Singular and Subsingular Vectors of the Topological N=2 Superconformal Algebra
• Extended chiral algebras in the SU(2)_0 WZNW model
• Lectures on conformal field theory and Kac-Moody algebras
• Singular vectors of the $W{A}_2$ algebra
• Extended multiplet structure in Logarithmic Conformal Field Theories