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R-operator, co-product and Haar-measure for the modular double of U_q(sl(2,R))

A. Bytsko·J. Teschner
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Abstract

A certain class of unitary representations of U_q(sl(2,R)) has the property of being simultanenously a representation of U_{tilde{q}}(sl(2,R)) for a particular choice of tilde{q}(q). Faddeev has proposed to unify the quantum groups U_q(sl(2,R)) and U_{tilde{q}}(sl(2,R)) into some enlarged object for which he has coined the name ``modular double''. We study the R-operator, the co-product and the Haar-measure for the modular double of U_q(sl(2,R)) and establish their main properties. In particular it is shown that the Clebsch-Gordan maps constructed in [PT2] diagonalize this R-operator.

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A. Bytsko, J. Teschner. 2002-08-25. R-operator, co-product and Haar-measure for the modular double of U_q(sl(2,R)). https://doi.org/10.1007/s00220-003-0894-5

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