
Journal of Lie Theory 32 (2022), No. 1, 281300 Copyright Heldermann Verlag 2022 Maximal Antipodal Sets of F_{4} and FI Yuuki Sasaki Dept. of Liberal Arts, National Institute of Technology, Tokyo College, Tokyo, Japan y_sasaki@tokyoct.ac.jp [Abstractpdf] 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. [ Fulltextpdf (197 KB)] for subscribers only. 