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We prove uniqueness of the essential order for stratified algebras havingsimple preserving duality, generalizing a recent result of Coulembier forquasi-hereditary algebras. We apply this to classify, up to equivalence,regular integral blocks of $\mathcal{S}$-subcategories in the BGG category$\mathcal{O}$. We also describe various homological invariants of these blocks.

Essential orders on stratified algebras with duality and $\mathcal{S}$-subcategories in $\mathcal{O}$