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A classification is given of the exceptional $\mathbb{Z}_2 \times\mathbb{Z}_2$-symmetric spaces $G/K$ by A.Kollross, where $G$ is an exceptionalcompact Lie group or $S\!pin(8)$, and moreover the structure of $K$ isdetermined as Lie algebra. In the present article, we give a pair of commutinginvolutive automorphisms (involutions) $\tilde{\sigma}, \tilde{\tau}$ of $G$concretely and determine the structure of group $G^{\sigma} \cap G^{\tau}$corresponding to Lie algebra $\mathfrak{g}^\sigma \cap \mathfrak{g}^\tau$,where $G$ is an exceptional compact Lie group. Thereby, we realize exceptional$\mathbb{Z}_2 \times \mathbb{Z}_2$-symmetric spaces, globally.

Realizations of globally exceptional $\mathbb{Z}_2 \times \mathbb{Z}_2$- symmetric spaces