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This is excellent. The existence of a minimal model requires $H^0(\mathcal{A})=\mathbb{Q}$. Is it possible to weaken this condition, say $ H^0(\mathcal{A})=\mathbb{Q}^n$? Best, Oliver
$K$ orbits on $G/P$ are studied in the book if Adams-Barbasch-Vogan: The Langlands Classification and Irreducible Characters for Real Reductive Groups.
