Involutions of compact Riemannian 4-symmetric spaces

Abstract

Let $G/H$ be a compact 4-symmetric space of inner type such that the dimension of the center $Z(H)$ of $H$ is at most one. In this paper we shall classify involutions of $G$ preserving $H$ for the case where $\dim Z(H)=0$, or $H$ is a centralizer of a toral subgroup of $G$.