On the relation between the modular double of U_q(sl(2,R)) and the quantum Teichmueller theory

Abstract

We exhibit direct relations between the modular double of U_q(sl(2,R)) and the quantum Teichmueller theory. Explicit representations for the fusion- and braiding operations of the quantum Teichmueller theory are immediate consequences. Our results include a simplified derivation of the Clebsch-Gordan decomposition for the principal series of representation of the modular double of U_q(sl(2,R)).

arXiv comment40 pages, 30 figures

References in corpus (4)

• Quantization of models with non-compact quantum group symmetry. Modular XXZ magnet and lattice sinh-Gordon model
• Liouville bootstrap via harmonic analysis on a noncompact quantum group
• On the relation between quantum Liouville theory and the quantized Teichm"uller spaces
• Dual Teichm\" uller spaces

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