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Perverse sheaves on Grassmannians. (English) Zbl 1009.32019

The author gives a very precise and explicit description of the quiver category of perverse sheaves constructible with respect to the Schubert stratification on a Hermitian symmetric space \(X\) of type A (a Grassmannian) and of type B (an isotropic Grassmannian). He uses microlocal techniques and the action of the Borel group on the conormal variety to the Schubert stratification of \(X\). He also discusses why his methods fail for a general flag variety \(G/B\).

MSC:

32S60 Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects)
32C38 Sheaves of differential operators and their modules, \(D\)-modules
35A27 Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
14M15 Grassmannians, Schubert varieties, flag manifolds
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