Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Realization of globally exceptional Riemannian $4$-symmetric space
  $E_8/(E_8)^{\sigma'_{4}}$   The compact simply connected Riemannian 4-symmetric spaces were classified by
J.A. Jim{\'{e}}nez. As homogeneous manifolds, these spaces are of the $G/H$,
where $G$ is a connected compact simple Lie group with an automorphism
$\tilde{\gamma}$ of oder 4 and $H$ is a fixed points subgroup $G^\gamma$ of
$G$. In the present article, for the exceptional compact Lie group $G=E_8$, we
give the explicit form of automorphism of order 4 induced by the
$\boldsymbol{R}$-linear transformation $\sigma'_{4}$ and determine the
structure of the group $(E_8)^{\sigma'_{4}}$. Thereby, we realize the globally
exceptional Riemannian $4$-symmetric space $E_8/(E_8)^{\sigma'_{4}}$.

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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
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The categories of this paper are: physics