  The SU(3) irreducible representations (irreps) are characterised by the
(lambda, mu) Elliott quantum numbers, which are necessary for the extraction of
the nuclear deformation, the energy spectrum and the transition probabilities.
These irreps can be calculated through a code which requires high computational
power. In the following text a hand-writing method is presented for the
calculation of the highest weight (h.w.) irreps, using two different sets of
magic numbers, namely proxy-SU(3) and three-dimensional isotropic harmonic
oscillator.
