Maximal antipodal sets related to 𝐺₂

Tanaka, Makiko; Tasaki, Hiroyuki; Yasukura, Osami

doi:10.1090/proc/15989

Maximal antipodal sets related to $G_{2}$
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by Makiko Sumi Tanaka, Hiroyuki Tasaki and Osami Yasukura PDF

Proc. Amer. Math. Soc. 150 (2022), 4533-4542 Request permission

Abstract:

We explicitly describe maximal antipodal sets of Riemannian symmetric spaces related to the compact connected simple Lie group of type $G_{2}$ by realizing it as the automorphism group of the octonions. Using these explicit descriptions we observe a close relation between maximal antipodal sets of the associative Grassmannian of the octonions and the Fano plane.

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