Duality and quantum groups

DOI10.1016/0550-3213(90)90116-UzbMath0764.17021MaRDI QIDQ1201685

Cesar A. Gómez, Luis Álvarez-Gaumé

Publication date: 17 January 1993

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

zbMATH Keywords

dualityquantum groupsknot invariantsrational conformal field theoriesWess-Zumino-Witten modelsWZW models

Mathematics Subject Classification ID

Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Applications of Lie (super)algebras to physics, etc. (17B81)

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Cites Work

• Unnamed Item
• Unnamed Item
• Quantum group interpretation of some conformal field theories
• Fusion rules and modular transformations in 2D conformal field theory
• Braid matrices and structure constants for minimal conformal models
• Unitary representations of the Virasoro and super-Virasoro algebras
• A \(q\)-analogue of \(U(\mathfrak{gl}(N+1))\), Hecke algebra, and the Yang-Baxter equation
• Vertex operators in the conformal field theory on \(\mathbb P^1\) and monodromy representations of the braid group
• Hecke algebra representations of braid groups and link polynomials
• The Yang-Baxter equation and invariants of links
• \(c=I\) conformal field theories on Riemann surfaces
• Modular invariant partition functions in two dimensions
• Current algebras and Wess-Zumino model in two dimensions
• Hecke algebras of type \(A_ n\) and subfactors
• Locality of conformal fields in two dimensions: Exchange algebra on the light-cone
• Index for subfactors
• Modular invariance and the fusion algebra