Journal of Lie Theory

no. 1
Maximal Antipodal Sets of F4 and FI
Journal of Lie Theory, Volume 32 (2022) no. 1, pp. 281-300
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 $FI$.
DOI: 10.5802/jolt.1231
Classification: 53C35,22E40
Keywords: Antipodal set, symmetric space, compact Lie group 
@article{JOLT_2022_32_1_a14,
     author = {Y. 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},
     doi = {10.5802/jolt.1231},
     zbl = {1498.53080},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1231/}
}
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Y. Sasaki. Maximal Antipodal Sets of F4 and FI. Journal of Lie Theory, Volume 32 (2022) no. 1, pp. 281-300. doi: 10.5802/jolt.1231

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