On the relation between the modular double of Uq(sl(2,R)) and the quantum Teichmueller theory
Abstract
We exhibit direct relations between the modular double of Uq(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 Uq(sl(2,R)).
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