Decomposition of compact exceptional Lie groups into their maximal tori

Abstract

In this paper we treat the intersection of fixed point subgroups by the involutive automorphisms of exceptional Lie group $G=F_4,E_6,E_7$. We shall find involutive automorphisms of $G$ such that the connected component of the intersection of those fixed point subgroups coincides with the maximal torus of $G$.

10 pages