Hyperplane section OP^2_0 of the complex Cayley plane as the homogeneous space F_4/P_4

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F11%3A10104555" target="_blank" >RIV/00216208:11320/11:10104555 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Hyperplane section OP^2_0 of the complex Cayley plane as the homogeneous space F_4/P_4
Original language description
We prove that the exceptional complex Lie group ${mathrm{F}_4}$ has a transitive action on the hyperplane section of the complex Cayley plane ${mathbb{O}mathbb{P}}^2$. Although the result itself is not new, our proof is elementary and constructive. Weuse an explicit realization of the vector and spin actions of ${mathrm{Spin}}(9,mathbb{C})leq {mathrm{F}_4}$. Moreover, we identify the stabilizer of the ${mathrm{F}_4}$-action as a parabolic subgroup ${mathrm{P}_4}$ (with Levi factor $mathrm{B_3T_1}$) of the complex Lie group ${mathrm{F}_4}$. In the real case we obtain an analogous realization of ${mathrm{F}_4}^{(-20)}/P$.
Czech name
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Czech description
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Project
<a href="/en/project/GA201%2F08%2F0397" target="_blank" >GA201/08/0397: Algebraic methods in geometry and topology</a>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP) Z - Vyzkumny zamer (s odkazem do CEZ) S - Specificky vyzkum na vysokych skolach

Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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