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Automorphisms of homogeneous space $F_4/P_{\{\beta_2\}}$ over the exceptional group $F_4$

Let $F_4$ be the connected, simply connected, simple, complex, linear algebraic group of type $\mathsf{F}_4$, with Dynkin diagram $$ \beta_1-\beta_2\Rightarrow\beta_3-\beta_4\,. $$ Let $P_{\{\beta_2\}}...
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