2026-06-28T14:59:30Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/1209242025-06-04T23:48:58Zcom_20.500.14352_14col_20.500.14352_15

On the vanishing of the hyperdeterminant under certain symmetry conditions Arrondo Esteban, Enrique Tocino, Alicia 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 ∗ ⊗ (d) ... ⊗ V ∗ = ⊗ λ Wλ(X, K) according to the different partitions λ of d, i.e. the different representations of Sd. In this paper we first give a decomposition W(d−1,1)(V, K) = ⊗ d−1 i=1 Wi (d−1,1)(V, K). We finally 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. 2025-06-04T17:09:48Z 2025-06-04T17:09:48Z 2025-06-04T17:09:48Z 2025 journal article https://hdl.handle.net/20.500.14352/120924 0021-8693 10.1016/j.jalgebra.2024.11.018 eng PID2021-124440NB FQM336 http://creativecommons.org/licenses/by/4.0/ open access Attribution 4.0 International Elsevier