A new look at the classification of the tri-covectors of a 6-dimensional symplectic space

Let F be a field of characteristic ≠2 and 3, let V be a F-vector space of dimension 6, and let Ω∈∧2V∗ be a non-degenerate form. A system of generators for polynomial invariant functions under the tensorial action of the group Sp(Ω) on ∧3V∗, is given explicitly. Applications of these results to the normal forms of De Bruyn-Kwiatkowski and Popov are given.