Rational orbits of primitive trivectors in dimension six

Abstract

Let $G=\operatorname{GL}(1)\times \mathrm{GSp}(6)$ and $V$ be the irreducible representation of $G$ of dimension 14 over a field of characteristic not equal to 2,3. This is an irreducible prehomogeneous vector space. We determine generic rational orbits and their stabilizers of this prehomogeneous vector space.