Geodesic
Maximal Antipodal Sets of F4 and FI
Yuuki Sasaki1
1Dept. of Liberal Arts, National Institute of Technology, Tokyo College, Tokyo, Japan
Journal of Lie Theory, Tome 32 (2022) no. 1, pp. 281-300

Voir la notice de l'article provenant de la source Heldermann Verlag

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 $FI$.
Classification : 53C35,22E40
Mots-clés : Antipodal set, symmetric space, compact Lie group

Yuuki Sasaki  1

1 Dept. of Liberal Arts, National Institute of Technology, Tokyo College, Tokyo, Japan 
Yuuki Sasaki. Maximal Antipodal Sets of F4 and FI. Journal of Lie Theory, Tome 32 (2022) no. 1, pp. 281-300. http://geodesic.mathdoc.fr/item/JOLT_2022_32_1_a14/
@article{JOLT_2022_32_1_a14,
     author = {Yuuki Sasaki},
     title = {Maximal {Antipodal} {Sets} of {F\protect\textsubscript{4}} and {FI}},
     journal = {Journal of Lie Theory},
     pages = {281--300},
     year = {2022},
     volume = {32},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2022_32_1_a14/}
}
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