Adjoint boson realization of SU(N) and a family of structural zeros of 6j coefficients

Abstract

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.