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 geometry perverse sheaves, microlocal geometry

MSC Classifications:

32S60, 32C38, 35A27 show english descriptions Stratifications; constructible sheaves; intersection cohomology [See also 58Kxx]
Sheaves of differential operators and their modules, $D$-modules [See also 14F10, 16S32, 35A27, 58J15]
Microlocal methods; methods of sheaf theory and homological algebra in PDE [See also 32C38, 58J15] 32S60 - Stratifications; constructible sheaves; intersection cohomology [See also 58Kxx]
32C38 - Sheaves of differential operators and their modules, $D$-modules [See also 14F10, 16S32, 35A27, 58J15]
35A27 - Microlocal methods; methods of sheaf theory and homological algebra in PDE [See also 32C38, 58J15]

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