Fixed points subgroups $G^{\sigma,\sigma'}$ by two involutive automorphisms $\sigma$, $\sigma'$ of exceptional compact Lie group $G$, Part II, $G = E_8$

Toshikazu Miyashita

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arXiv · 1012.3517

Fixed points subgroups $G^{\sigma,\sigma'}$ by two involutive automorphisms $\sigma$, $\sigma'$ of exceptional compact Lie group $G$, Part II, $G = E_8$

Toshikazu Miyashita

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Abstract

For the simply connected compact exceptional Lie group $E_8$, we determine the structure of subgroup $(E_8)^{\sigma, \sigma'}$ of $E_8$ which is the intersection $(E_8)^\sigma \cap (E_8)^{\sigma'}$. Then the space $E_8/(E_8)^{\sigma, \sigma'}$ is the exceptional $\mathbb{Z}_2 \times \mathbb{Z}_2$- symmetric space of type EVIII-VIII-VIII, and that we give two involutions $\sigma, \sigma'$ for the space $E_8/(E_8)^{\sigma, \sigma'}$ concretely.

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BibTeX RIS

Toshikazu Miyashita. 2010-12-16. Fixed points subgroups $G^{\sigma,\sigma'}$ by two involutive automorphisms $\sigma$, $\sigma'$ of exceptional compact Lie group $G$, Part II, $G = E_8$. https://arxiv.org/abs/1012.3517

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