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

摘要

We determine the Clebsch-Gordan and Racah-Wigner coefficients for continuous series of representations of the quantum deformed algebras U_{q}\left ( sl\left ( 2 \right ) \right ) and U_{q}\left ( osp\left ( 1\mid 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.