Exceptional collections on isotropic Grassmannians
  We introduce a new construction of exceptional objects in the derived category of coherent sheaves on a compact homogeneous space of a semisimple algebraic group and show that it produces exceptional collections of the length equal to the rank of the Grothendieck group on homogeneous spaces of all classical groups. 
Alexander Kuznetsov and Alexander Polishchuk
math.AG math.RT