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The consequences of the attractive, short-range nucleon-nucleon (NN)interaction on the wave functions of the Elliott SU(3) and the proxy-SU(3)symmetry are discussed. The NN interaction favors the most symmetric spatialSU(3) irreducible representation, which corresponds to the maximal spatialoverlap among the fermions. The percentage of the symmetric components out ofthe total in an SU(3) wave function is introduced, through which it is found,that no SU(3) irrep is more symmetric than the highest weight irrep for acertain number of valence particles in a three dimensional, isotropic, harmonicoscillator shell. The consideration of the highest weight irreps in nuclei andin alkali metal clusters, leads to the prediction of a prolate to oblate shapetransition beyond the mid-shell region.

Why nuclear forces favor the highest weight irreducible representations of the fermionic SU(3) symmetry