On the structure of unitary conformal field theory. II: Representation theoretic approach

DOI10.1007/BF02099872zbMath0704.46051MaRDI QIDQ916982

Elsie Sterbin Gottlieb

Publication date: 1990

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

zbMATH Keywords

knotsquantum groupslinkstensor product representationsChiral fusionClebsch-Gordan operatorsco-multiplicationsirreducible subrepresentations of a chiral algebrarepresentation theory of chiral algebrasTwo-dimensional, unitary rational conformal field theoryYang-Baxter (braid) matrices

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Applications of Lie groups to the sciences; explicit representations (22E70) Applications of functional analysis in quantum physics (46N50)

Related Items (13)

Matrix product approximations to conformal field theories ⋮ Comments on fusion matrix in \(\mathbf{N} = 1\) super Liouville field theory ⋮ Classical limit of irregular blocks and Mathieu functions ⋮ Classical origin of quantum group symmetries in Wess-Zumino-Witten conformal field theory ⋮ Tetrahedral symmetry of \(6j\)-symbols in fusion categories ⋮ Solving Heun's equation using conformal blocks ⋮ Irregular Uq (sl(3)) representations at roots of unity via Gel’fand–(Weyl)–Zetlin basis ⋮ SOME REMARKS ON D-BRANES AND DEFECTS IN LIOUVILLE AND TODA FIELD THEORIES ⋮ A construction of topological quantum field theories from \(6j\)-symbols ⋮ S 4 symmetry of 6j symbols and Frobenius–Schur indicators in rigid monoidal C* categories ⋮ Conformal field algebras with quantum symmetry from the theory of superselection sectors ⋮ Branes: From free fields to general backgrounds ⋮ New Semiclassical Non-Abelian Vertex Operators for Chiral and Nonchiral WZW Theory

Cites Work

• Unnamed Item
• Fusion rules and modular transformations in 2D conformal field theory
• Braid matrices and structure constants for minimal conformal models
• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• Details of the non-unitary proof for highest weight representations of the Virasoro algebra
• 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 A-D-E classification of minimal and \(A_ 1^{(1)}\) conformal invariant theories
• Infinite conformal symmetry in two-dimensional quantum field theory
• Modular invariant partition functions in two dimensions
• Current algebras and Wess-Zumino model in two dimensions
• Locality of conformal fields in two dimensions: Exchange algebra on the light-cone
• Etiology of IRF models
• On the structure of unitary conformal field theory. I: Existence of conformal blocks
• TWO-DIMENSIONAL CONFORMAL FIELD THEORY AND THREE-DIMENSIONAL TOPOLOGY

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