ABSTRACT
In a recent paper [1] we have constructed the spin and tensor representations of https://www.w3.org/1998/Math/MathML"> SO ( 4 ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429076619/c00d8d0d-b3a0-431a-a3c2-e044ea15f7a5/content/eq5870.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> from whichthe invariant weight can be derived for the BarrettCrane model in quantum gravity. By analogy with the https://www.w3.org/1998/Math/MathML"> SO ( 4 ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429076619/c00d8d0d-b3a0-431a-a3c2-e044ea15f7a5/content/eq5871.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> group, we present the complexified Clebsch-Gordan coefficients in order to construct the BiedenharnDolginov function for the https://www.w3.org/1998/Math/MathML"> SO ( 3,1 ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429076619/c00d8d0d-b3a0-431a-a3c2-e044ea15f7a5/content/eq5872.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> group and the spherical function as the Lorentz invariant weight of the model.
