Self-dual continuous series of representations for $U_{q}(sl(2))$ and $U_{q}(osp(1\mid 2))$

We determine the Clebsch-Gordan and Racah-Wigner coefficients for continuous series of representations of the quantum deformed algebras $U_{q}(sl(2))$ and $U_{q}(osp(1\mid 2))$. While our results for the former algebra reproduce formulas by Ponsot and Teschner, the expressions for the orthosymplectic algebra are new. Up to some normalization factors, the associated Racah-Wigner coefficients are shown to agree with the fusing matrix in the Neveu-Schwarz sector of N =1 supersymmetric Liouville field theory.