As an example, consider the projection Pαβγ ≡ T⟨αβγ⟩ of a three index tensor Tαβγ onto the Young tableaux
|-|-| |-|-. ---
This projection is given by
1 Pαβγ = 3(Tαβγ + Tβαγ − Tγβα − Tβγα ),
which clearly satisfies
P αβγ = − P γβα, P[αβγ] = 0.
Note also that Pαβγ ⁄= Pβαγ.