The hyperdeterminant vanishes for 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 ${\wedge }^{p}V\subseteq V^{\otimes p}$ with $p\ge 3$ then it vanishes. The hyperdeterminant also vanishes when we restrict it to the space ${\Gamma }^{\lambda }V\otimes S_{\lambda }V\subseteq V^{\otimes p}$ where $\lambda$ is a Young diagram with p boxes and ${\lambda }_2\ge 2$ or ${\lambda }_3\ge 1$.

6 pages

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