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

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

2010-12-16

arxiv.org/abs/1012.3517v1

Kyushu J.Math.64(2010),221-237

Mathematics

Differential Geometry

16pages

Scientific paper

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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