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

TL;DR

This paper introduces a new universal formula for the Racah-Wigner symbol of Uq(osp(1|2)), unifying various sectors and reproducing known results through analytic continuation, advancing the understanding of supersymmetric quantum groups.

Contribution

It provides a novel, elegant formula for the Racah-Wigner symbol applicable to all self-dual continuous series representations of Uq(osp(1|2).

Findings

Unified expression for Racah-Wigner symbols in supersymmetric Liouville theory.

Reproduces known finite-dimensional Racah-Wigner coefficients via analytic continuation.

Connects NS and R sectors through a universal formula.

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.