Journal of Lie Theory 32 (2022), No. 1, 281--300
Copyright Heldermann Verlag 2022
Maximal Antipodal Sets of F4 and FI
Yuuki Sasaki
Dept. of Liberal Arts, National Institute of Technology, Tokyo College, Tokyo, Japan
y_sasaki@tokyo-ct.ac.jp
[Abstract-pdf]
We explicitly classify congruent classes of maximal antipodal sets of $F_{4}$ by using the Jordan algebra $H_{3}(\mathbb{O})$. Moreover, we give a realization of the compact symmetric space of type $FI$ as a totally geodesic submanifold in a Grassmannian $G_{15}(H_{3}(\mathbb{O}))$, where $G_{15}(H_{3}(\mathbb{O}))$ is the set of all subspaces of dimension 15 in $H_{3}(\mathbb{O})$. In this realization, we explicitly classify congruent classes of maximal antipodal sets of $FI$.
Keywords: Antipodal set, symmetric space, compact Lie group.
MSC: 53C35,22E40.
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