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Communications in Mathematical Physics

, Volume 161, Issue 3, pp 597–630 | Cite as

The quantum group structure of 2D gravity and minimal models II: The genus-zero chiral bootstrap

  • Eugène Cremmer
  • Jean-Loup Gervais
  • Jean-François Roussel
Article

Abstract

The chiral operator-algebra of the quantum-group-covariant operators (of vertex type) is completely worked out by making use of the operator-approach suggested by the Liouville theory, where the quantum-group symmetry is explicit. This completes earlier articles along the same line. The relationship between the quantum-group-invariant (of IRF type) and quantum-group-covariant (of vertex type) chiral operator-algebras is fully clarified, and connected with the transition to the shadow world for quantum-group symbols. The corresponding 3-j symbol dressing is shown to reduce to the simpler transformation of Babelon and one of the authors (J.-L. G.) in a suitable infinite limit defined by analytic continuation. The above two types of operators are found to coincide when applied to states with Liouville momenta going to ∞ in a suitable way. The introduction of quantum-group-covariant operators in the three dimensional picture gives a generalization of the quantum-group version of discrete three-dimensional gravity that includes tetrahedra associated with 3-j symbols and universalR-matrix elements. Altogether the present work and a previous parallel article gives the concrete realization of Moore and Seiberg's scheme that describes the chiral operator-algebra of two-dimensional gravity and minimal models.

Keywords

Neural Network Quantum Computing Analytic Continuation Group Structure Minimal Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Eugène Cremmer
    • 1
  • Jean-Loup Gervais
    • 1
  • Jean-François Roussel
    • 1
  1. 1.Laboratoire de Physique Théorique de l'École Normale SupérieureParis Cedex 05France

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