Clebsch-Gordan and Racah-Wigner coefficients for a continuous series of representations of U_q(sl(2,R))

Details Clebsch-Gordan and Racah-Wigner coefficients for a continuous series of representations of U_q(sl(2,R)) Clebsch-Gordan and Racah-Wigner coefficients for a continuous series of representations of U_q(sl(2,R))

2000-07-15

arxiv.org/abs/math/0007097v2

Commun.Math.Phys. 224 (2001) 613-655

Mathematics

Quantum Algebra

39 pages, AMS-Latex; V2: Added comments and references concerning relation to Faddeev's modular double, minor corrections, ver

Scientific paper

10.1007/PL00005590

The decomposition of tensor products of representations into irreducibles is studied for a continuous family of integrable operator representations of $U_q(sl(2,R)$. It is described by an explicit integral transformation involving a distributional kernel that can be seen as an analogue of the Clebsch-Gordan coefficients. Moreover, we also study the relation between two canonical decompositions of triple tensor products into irreducibles. It can be represented by an integral transformation with a kernel that generalizes the Racah-Wigner coefficients. This kernel is explicitly calculated.

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