Singular vectors of \(\mathcal W\) algebras via DS reduction of \(A^{(1)}_2\)

DOI10.1016/0550-3213(94)90217-8zbMath1020.81623OpenAlexW1656456106MaRDI QIDQ1571387

Alexander Ch. Ganchev, Paolo Furlan, Valentina B. Petkova

Publication date: 10 July 2000

Published in: Nuclear Physics. B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0550-3213(94)90217-8

Mathematics Subject Classification ID

Virasoro and related algebras (17B68) Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10)

Related Items (5)

Families of singular and subsingular vectors of the topological \(N=2\) superconformal algebra ⋮ Fusion rules for admissible representations of affine algebras: the case of \(A_2^{(1)}\) ⋮ On structure constants of \(\text{sl}(2)\) theories. ⋮ On principal admissible representations and conformal field theory ⋮ Classification of irreducible modules for Bershadsky–Polyakov algebra at certain levels

Cites Work

• Quantization of the Drinfel'd-Sokolov reduction.
• Hidden SL(n) symmetry in conformal field theories
• Singular vectors of the \(WA_2\) algebra.
• Extensions of the Virasoro algebra constructed from Kac-Moody algebras using higher order Casimir invariants
• Structure of representations with highest weight of infinite-dimensional Lie algebras
• Characters and fusion rules for \(W\)-algebras via quantized Drinfeld- Sokolov reduction
• On \(sl(3)\) reduction, quantum gauge transformations, and \(W\)-algebra singular vectors
• Semi-infinite cohomology of \({\mathcal W}\)-algebras
• Quantization and representation theory of finite \(W\) algebras
• The relation between quantum \(W\) algebras and Lie algebras
• Covariant differential equations and singular vectors in Virasoro representations
• Toda theory and \({\mathcal W}\)-algebra from a gauged WZNW point of view
• Conformal field theories via Hamiltonian reduction
• A MATHEMATICA™ PACKAGE FOR COMPUTING OPERATOR PRODUCT EXPANSIONS

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