Racah Algebra for an Arbitrary Group

Abstract

3j‐ and 6j‐symbols are studied for a general group without assuming that the group is ambivalent or multiplicity‐free. The choice of multiplicity label r that distinguishes the equivalent irreducible representations that may arise in a Kronecker product of irreducible representations is left arbitary and no special choices of phase are made. It is found that the 3j‐ and 6j‐symbols obtained have essentially the same properties as the familiar 3j‐ and 6j‐symbols for the rotation group in three dimensions.