R-operator, co-product and Haar-measure for the modular double of Uq(sl(2,R))
Abstract
A certain class of unitary representations of Uq(sl(2,R)) has the property of being simultanenously a representation of Utildeq(sl(2,R)) for a particular choice of tildeq(q). Faddeev has proposed to unify the quantum groups Uq(sl(2,R)) and Utildeq(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 Uq(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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