For the fundamental boson realization of SU(N) in its principal SO(3) basis, the generators of SU(N) are SO(3) tensor operators constructed out of one single type of boson, namely a boson with SO(3) multiplet label (N−1)/2. Here, the adjoint boson realization of SU(N) is given: this time the SO(3) tensor operators are constructed by means of N−1 types of bosons [those with SO(3) labels 1,2,..., N−1]. The validity of this realization depends upon a new identity between 6j coefficients. From this realization, or equivalently from this new identity, one can deduce the existence of a family of structural zeros of 6j coefficients.

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