Fusion and singular vectors in \(A_ 1^{(1)}\) highest weight cyclic modules

DOI10.1007/BF02097060zbMath0786.17018arXivhep-th/9201079MaRDI QIDQ1803944

Michel Bauer, Nir Sochen

Publication date: 29 June 1993

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/9201079

zbMATH Keywords

highest weight modulesvertex operatorsaffine Lie algebradescent equationsfusion of primary fieldssingular vectors in Verma modulesWess-Zumino conformal field theories

Mathematics Subject Classification ID

Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Virasoro and related algebras (17B68) Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Vertex operators; vertex operator algebras and related structures (17B69)

Related Items (8)

CONSTRUCTION FORMULAE FOR SINGULAR VECTORS OF THE TOPOLOGICAL AND OF THE RAMOND N = 2 SUPERCONFORMAL ALGEBRAS ⋮ Fusion rules and singular vectors of the \(\text{osp}(1|2)\) current algebra ⋮ Macdonald index and chiral algebra ⋮ Modular data and Verlinde formulae for fractional level WZW models. II ⋮ String correlators on \(\mathrm{AdS}_3\): four-point functions ⋮ \(\hat{\mathfrak sl}(2)_{-\frac{1}{2}}\): a case study ⋮ On principal admissible representations and conformal field theory ⋮ Representations of infinite-dimensional algebras and conformal field theory: From \(N=2\) to \(\widehat{sl} (2|1)\)

Cites Work

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• Hidden SL(n) symmetry in conformal field theories
• Fock representations and BRST cohomology in \(\mathrm{SL}(2)\) current algebra
• Lie algebras and equations of Korteweg-de Vries type
• Infinite conformal symmetry in two-dimensional quantum field theory
• Current algebras and Wess-Zumino model in two dimensions
• Structure of representations with highest weight of infinite-dimensional Lie algebras
• Covariant differential equations and singular vectors in Virasoro representations
• Lie Groups, Lie Algebras, and Cohomology. (MN-34), Volume 34

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