On the exactness of Kostant-Kirillov form and the second cohomology of   nilpotent orbits
  We give a criterion for the Kostant-Kirillov form on an adjoint orbit in a real semisimple Lie group to be exact. We explicitly compute the second cohomology of all the nilpotent adjoint orbits in every complex simple Lie algebras. 
Indranil Biswas and Pralay Chatterjee
math.GR math.SG