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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.06603 |
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Table of Contents:
- Given a vector space $V$ over a field $\K$ whose characteristic is coprime with $d!$, let us decompose the vector space of multilinear forms $V^*\otimes\overset{\text(d)}{\ldots}\otimes V^*=\bigoplus _λW_λ(X,\K)$ according to the different partitions $λ$ of $d$, i.e. the different representations of $S_d$. In this paper we first give a decomposition $W_{(d-1,1)}(V,\K)=\bigoplus_{i=1}^{d-1}W_{(d-1,1)}^i(V,\K)$. We finally prove the vanishing of the hyperdeterminant of any $F\in(\bigoplus_{λ\ne(d),(d-1,1)})\oplus W_{(d-1,1)}^i(V,\K)$. This improves the result in [10] and [1], where the same result was proved without this new last summand.