Perverse Sheaves on Grassmannians We compute the category of perverse sheaves on Hermitian symmetric spaces in types~A and D, constructible with respect to the Schubert stratification. The calculation is microlocal, and uses the action of the Borel group to study the geometry of the conormal variety $\Lambda$. Keywords:perverse sheaves, microlocal geometryCategories:32S60, 32C38, 35A27