Perverse sheaves over real hyperplane arrangements
نویسندگان
چکیده
منابع مشابه
Perverse Sheaves on Real Loop Grassmannians
The aim of this paper is to identify a certain tensor category of perverse sheaves on the real loop Grassmannian GrR of a real form GR of a connected reductive complex algebraic group G with the category of finite-dimensional representations of a reductive complex algebraic subgroup H of the dual group Ǧ. The root system of H is closely related to the restricted root system of GR. The fact that...
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Given a real finite hyperplane arrangement A and a point p not on any of the hyperplanes, we define an arrangement vo(A, p), called the valid order arrangement, whose regions correspond to the different orders in which a line through p can cross the hyperplanes in A. If A is the set of affine spans of the facets of a convex polytope P and p lies in the interior of P, then the valid orderings wi...
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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.
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The purpose of this article is to set foundations for decomposition numbers of perverse sheaves, to give some methods to calculate them in simple cases, and to compute them concretely in two situations: for a simple (Kleinian) surface singularity, and for the closure of the minimal non-trivial orbit in a simple Lie algebra. This work has applications to modular representation theory, for Weyl g...
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where t· x denotes the action of t on x. The set Xw is known to be a locally-closed c* -stable algebraic subvariety of X isomorphic to an affine space. The pieces Xw form a cell decomposition X = UWEW XW ' W E W, the socalled Bialynicki-Birula decomposition. We assume this decomposition to be an algebraic stratification of X (the closure of a cell may not be a union of cells, in general). Let ....
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ژورنال
عنوان ژورنال: Annals of Mathematics
سال: 2016
ISSN: 0003-486X
DOI: 10.4007/annals.2016.183.2.4