Self-dual Continuous Series of Representations for U_q(sl(2)) and U_q(osp(1|2))

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.

36 pages

References in corpus (5)

• On the fusion matrix of the N=1 Neveu-Schwarz blocks
• Braiding and fusion properties of the Neveu-Schwarz super-conformal blocks
• On the relation between the modular double of U_q(sl(2,R)) and the quantum Teichmueller theory
• Braiding properties of the N=1 super-conformal blocks (Ramond sector)
• Analytic continuation formulae for the BPZ conformal block

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