The super-rotation Racah–Wigner calculus revisited

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Abstract
It is shown that, since the finite dimensional representations of the super-rotation algebra are characterized by the superspin j and the parity λ of the representation space, all features of the Racah–Wigner calculus: Clebsch–Gordan coefficients, recoupling coefficients as well as the Wigner and Racah symbols depend on both j and λ. However, it is noticed that the dependence on the parities of the Wigner and Racah symbols can be factorized out into phases so that one can define parity-independent super S3−j and S6−j symbols. The properties of these symbols are analyzed, in particular, it is shown that the S6−j symbols possess a symmetry similar to the Regge symmetry satisfied by the rotation 6−j symbols. Analytical and numerical tables of the symbols are given for the lowest values of their arguments.

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