Given a vector space V over a field K whose characteris tic is coprime with d!, let us decompose the vector spa
of multilinear forms V ∗ ⊗ (d) ... ⊗ V ∗ =
λ Wλ(X, K) ac cording to the different partitions λ of d, i.e. the different
representations of Sd. In this paper we first give a decom position W(d−1,1)(V, K) = d
i=1 Wi
(d−1,1)(V, K). We final
prove the vanishing of the hyperdeterminant of any F ∈
(
λ =(d),(d−1,1)) ⊕ Wi
(d−1,1)(V, K). This improves the result
in [10] and [1], where the same result was proved without this
new last summand.
