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Hyperplane section \({\mathbb {O}\mathbb {P}}^2_0\) of the complex Cayley plane as the homogeneous space \({\text F}_4/{\text P}_4\). (English) Zbl 1249.32019
The authors present a transitive action of the exceptional complex Lie group \(F_4\) on the hyperplane section of the complex Cayley plane \({\mathbb {O}\mathbb {P}}^2\). Clifford algebras, spin groups and the representation theory are used.
MSC:
32M12 Almost homogeneous manifolds and spaces
14M17 Homogeneous spaces and generalizations
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