The hyperdeterminant vanishes on all but two Schur functors

We recall the notion of hyperdeterminant of a multidimensional matrix (tensor). We prove that if we restrict the hyperdeterminant to a skew-symmetric tensor ⋀pV⊆V⊗p with p≥3 then it vanishes. The hyperdeterminant also vanishes when we restrict it to the space Γλ⊗SλV⊂V⊗p where λ is a Young diagram with p boxes and λ2≥2 or λ3≥1.