For three and four identical fermions in harmonic models, only spatial wavefunctions belonging to the irreps A2 and E (for N=3) or A2, E and T1 (for N=4) are compatible with the antisymmetry principle.
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Allowed permutation symmetry in atomic and molecular wavefunctions. Simple examples
For three and four identical fermions in harmonic models, only spatial wavefunctions belonging to the irreps A2 and E (for N=3) or A2, E and T1 (for N=4) are compatible with the antisymmetry principle.