9. Highest Weight Structure on Categories of Perverse Sheaves
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Problem 9.1.
[Mautner] Is there a geometric proof (i.e. avoiding Geometric Satake) that \operatorname{Perv}_{\mathrm{sph}}(Gr, k) is highest-weight? -
Problem 9.2.
More generally, when is a category of perverse sheaves constructible with respect to a fixed stratification highest-weight? -
Problem 9.3.
[Braden–Mautner] Given a symplectic resolution \pi\colon Y \to X, with G = \operatorname{Aut}(X, \omega), consider the subcategory of \operatorname{Perv}_G(X, k) generated by subquotients of \pi_*\underline{k}_Y. When is this highest-weight?
Cite this as: AimPL: Sheaves and modular representations of reductive groups, available at http://aimpl.org/sheavemodular.