Define a full exceptional set in a triangulated category to be a partially ordered set of objects $\Delta_i$ which generate the category and such that $\text{Ext}^\bullet(\Delta_i, \Delta_j) = 0$ if $i < j$ and $\text{Ext}^\bullet(\Delta_i, \Delta_i) = k$.

Is there a known (nonequivariant) full quasiexceptional set on the full flag variety? Or partial flag varieties that are not $\mathbb{P}^n$?

Define a full exceptional set in a triangulated category to be a partially ordered set of objects $\Delta_i$ which generate the category and such that $\text{Ext}^\bullet(\Delta_i, \Delta_j) = 0$ unless $i \geq j$ and $\text{Ext}^\bullet(\Delta_i, \Delta_i) = k$.

Is there a known (nonequivariant) full exceptional set in coherent sheaves on the full flag variety? Or partial flag varieties that are not $\mathbb{P}^n$?