The image of the Lepowsky homomorphism for the group $F_4$

Alfredo Brega, Leandro Cagliero, Juan Tirao

Let $G_o$ be a semisimple Lie group, let $K_o$ be a maximal compact subgroup of $G_o$ and let $\mathfrak{k}\subset \mathfrak{g}$ denote the complexification of their Lie algebras. L…