Hyperplane section ${\mathbb{OP}}_0^2$ of the complex Cayley plane as the homogeneous space ${\mathrm{F}}_4/{\mathrm{P}}_4$

Peter Franek, Karel Pazourek, Vít Tuček

We prove that the exceptional complex Lie group $F_4$ has a transitive action on the hyperplane section of the complex Cayley plane ${\mathbb{OP}}^2$. Our proof is direct and constru…