The universal Racah-Wigner symbol for U q (osp(1|2))

Abstract

We propose a new and elegant formula for the Racah-Wigner symbol of self-dual continuous series of representations of Uq(osp(1|2)). It describes the entire fusing matrix for both NS and R sector of N=1 supersymmetric Liouville field theory. In the NS sector, our formula is related to an expression derived in [1]. Through analytic continuation in the spin variables, our universal expression reproduces known formulas for the Racah-Wigner coefficients of finite dimensional representations.