Applications of the Gel'fand-Moshinsky bases in unitary symmetry and its breaking

The Gel'fand-Moshinsky bases for the unitary irreducible representations of the SU3 group are applied to the unitary scheme for the classification of elementary particles and resonances. A unified method is given for the derivation of the matrix elements of the octet tensor operators in a way which makes transparent its application for other irreducible tensors. The results are given in a remarkably simple form. The systematic use of the basis provides a methodological alternative to the current tensorial methods.