Abstract
We determine the Clebsch-Gordan and Racah-Wigner coefficients for continuous series of representations of the quantum deformed algebras \( {\mathcal{U}}_q\left(sl(2)\right) \) and \( {\mathcal{U}}_q\left(osp\left(1\Big|2\right)\right) \). 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.
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Hadasz, L., Pawelkiewicz, M. & Schomerus, V. Self-dual continuous series of representations for \( {\mathcal{U}}_q\left(sl(2)\right) \) and \( {\mathcal{U}}_q\left(osp\left(1\Big|2\right)\right) \) . J. High Energ. Phys. 2014, 91 (2014). https://doi.org/10.1007/JHEP10(2014)091
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DOI: https://doi.org/10.1007/JHEP10(2014)091