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

2002/08/25 by A. Bytsko, J. Teschner · 1 citation
Mathematics · Physics and Astronomy · #math.QA #hep-th

paper · pdf · doi:10.1007/s00220-003-0894-5

published as Commun.Math.Phys. 240 (2003) 171-196 · 27 pages, LaTex (smfart.sty)

arxiv created 2002/08/25 · arxiv updated 2009/11/30

Abstract

A certain class of unitary representations of U_q(sl(2,R)) has the property of being simultanenously a representation of U_tildeq(sl(2,R)) for a particular choice of tildeq(q). Faddeev has proposed to unify the quantum groups U_q(sl(2,R)) and U_tildeq(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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