Determination of operator equivalents from irreducible tensors

A new method of derivation of operator equivalents is proposed, in which individual irreducible tensor components are expressed in terms of both real and complex unit tensors derived from real and complex (or bi) vectors. The method is extended to irreducible tensor operators which do not have full permutation symmetry and it is found that these are equivalent to totally symmetric tensor operators of rank equal to the angular momentum quantum number.