The hyperdeterminant vanishes on all but two Schur functors

Abstract

We recall the notion of hyperdeterminant of a multidimensional matrix (tensor). We prove that if we restrict the hyperdeterminant to a skew-symmetric tensor p V ⊆ 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.