Realization of globally exceptional Riemannian 4-symmetric space E₈/(E₈)^σ'₄

2015/06/11 by Miyashita, Toshikazu
#Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1506.03575

Abstract

The compact simply connected Riemannian 4-symmetric spaces were classified by J.A. Jiménez. As homogeneous manifolds, these spaces are of the G/H, where G is a connected compact simple Lie group with an automorphism γ of oder 4 and H is a fixed points subgroup G^γ of G. In the present article, for the exceptional compact Lie group G=E₈, we give the explicit form of automorphism of order 4 induced by the \boldsymbolR-linear transformation σ'₄ and determine the structure of the group (E₈)^σ'₄. Thereby, we realize the globally exceptional Riemannian 4-symmetric space E₈/(E₈)^σ'₄.

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