Self-dual continuous series of representations for U q s l 2 $$ {\mathcal{U}}_q\left(sl(2)\right) $$ and U q o s p 1 | 2 $$ {\mathcal{U}}_q\left(osp\left(1\Big|2\right)\right) $$

Abstract

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|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.