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Dec 13, 2018 at 6:32 comment added Francesco Polizzi Thank you very much for the answer, I will check the details.
Dec 12, 2018 at 21:31 comment added Francois Ziegler And both are special cases of the Borel-Weil-Tits embedding of $G/P_2$ into projective space of its geometric quantization, when endowed with its symplectic structure as coadjoint orbit of $\omega_2$, resp. ${n+1\choose 2}\omega_2$.
Dec 12, 2018 at 19:54 history answered Sasha CC BY-SA 4.0