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外文期刊>The journal of high energy physics
>Self-dual continuous series of representations for $$ {mathcal{U}}_qleft(sl(2)ight) $$ and $$ {mathcal{U}}_qleft(ospleft(1Big|2ight)ight) $$
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Self-dual continuous series of representations for $$ {mathcal{U}}_qleft(sl(2)ight) $$ and $$ {mathcal{U}}_qleft(ospleft(1Big|2ight)ight) $$
A bstract We determine the Clebsch-Gordan and Racah-Wigner coefficients for continuous series of representations of the quantum deformed algebras U q s l 2 $$ {mathcal{U}}_qleft(sl(2)ight) $$ and U q o s p 1 | 2 $$ {mathcal{U}}_qleft(ospleft(1Big|2ight)ight) $$ . 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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