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

Let $\mathbb{F}$ be a field of characteristic $\mathrm{\ne }2$ and $3$, let $V$ be a $\mathbb{F}$-vector space of dimension $6$, and let $\mathrm{\Omega }\in {\wedge }^2{V}^{\ast }$ be a non-degenerate form. A system of generators for polynomial invariant functions under the tensorial action of the group $Sp(\mathrm{\Omega })$ on ${\wedge }^3{V}^{\ast }$, is given explicitly. Applications of these results to the normal forms of De Bruyn-Kwiatkowski and Popov are given.