Exceptional collections of line bundles on projective homogeneous   varieties
  We construct new examples of exceptional collections of line bundles on the variety of Borel subgroups of a split semisimple linear algebraic group G of rank 2 over a field. We exhibit exceptional collections of the expected length for types A_2 and B_2=C_2 and prove that no such collection exists for type G_2. This settles the question of the existence of full exceptional collections of line bundles on projective homogeneous G-varieties for split linear algebraic groups G of rank at most 2. 
Alexey Ananyevskiy, Asher Auel, Skip Garibaldi, Kirill Zainoulline
math.AG math.KT