Abstract
In [3], a classification is given of the exceptional $\mathbf{Z}_2 \times \mathbf{Z}_2$-symmetric spaces $G/K$, where $G$ is an exceptional compact Lie group or $Spin(8)$, and moreover the structure of $K$ is determined as Lie algebra. In the present article, we give a pair of commuting involutive 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 $\mathbf{Z}_2 \times \mathbf{Z}_2$-symmetric spaces, globally.
Citation
Toshikazu Miyashita. "Realizations of globally exceptional $\mathbf{Z}_2 \times \mathbf{Z}_2$-symmetric spaces." Tsukuba J. Math. 38 (2) 239 - 311, March 2015. https://doi.org/10.21099/tkbjm/1429103724
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