Classification of nilpotent and semisimple fourvectors of a real eight-dimensional space

Emanuele Di Bella, Willem A. de Graaf, Andrea Santi

In 1981 Antonyan classified the orbits of SL$(8,\mathbb{C})$ on ${\bigwedge }^4{\mathbb{C}}^8$. This is an example of a $\theta$-group action as introduced and studied by Vinberg. The orbit…