Exotic tilting sheaves, parity sheaves on affine Grassmannians, and the Mirković–Vilonen conjecture
نویسندگان
چکیده
منابع مشابه
Perverse Sheaves on Grassmannians
We give a complete quiver description of 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 Λ.
متن کاملPerverse sheaves on affine Grassmannians and Langlands duality
In this paper we outline a proof of a geometric version of the Satake isomorphism. Namely, given a connected, complex algebraic reductive group G we show that the tensor category of representations of the dual group G is naturally equivalent to a certain category of perverse sheaves on the affine Grassmannian of G. This can be extended to give a topological realization of algebraic representati...
متن کاملModular perverse sheaves on flag varieties I: tilting and parity sheaves
In this paper we prove that the category of parity complexes on the flag variety of a complex connected reductive group G is a “graded version” of the category of tilting perverse sheaves on the flag variety of the dual group Ǧ, for any field of coefficients whose characteristic is good for G. We derive some consequences on Soergel’s modular category O, and on multiplicities and decomposition n...
متن کاملParity Sheaves
Given a stratified variety X with strata satisfying a cohomological parity-vanishing condition, we define and show the uniqueness of “parity sheaves”, which are objects in the constructible derived category of sheaves with coefficients in an arbitrary field or complete discrete valuation ring. If X admits a resolution also satisfying a parity condition, then the direct image of the constant she...
متن کاملMorse Theory and Tilting Sheaves
Tilting perverse sheaves arise in geometric representation theory as natural bases for many categories. (See [1] or Section 3 below for definitions and some background results.) For example, for category O of a complex reductive group G, tilting modules correspond to tilting sheaves on the Schubert stratification S of the flag variety B. In this setting, there are many characterizations of tilt...
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ژورنال
عنوان ژورنال: Journal of the European Mathematical Society
سال: 2018
ISSN: 1435-9855
DOI: 10.4171/jems/812