Symmetry Properties of the 3j-Symbols for an Arbitrary Group

Abstract

The symmetry properties of the 3j‐symbols are studied for an arbitrary compact group. It is shown that when the three j's are all inequivalent it is possible to choose 3j‐symbols which are invariant under any permutation of the j's and of the corresponding m's (generalized magnetic quantum numbers). When two of the three j's are equivalent, the 3j‐symbols can be chosen in such a way that at most a minus sign appears when the j's and m's are permuted. It is also shown that when the three j's are equivalent it is in general not possible to choose the 3j‐symbol such that its absolute value is invariant under every permutation of the m's.