The affine flag variety
نویسنده
چکیده
منابع مشابه
On GKM Description of the Equivariant Cohomology of Affine Flag Varieties and Affine Springer Fibers
For a projective variety endowed with a torus action, the equivariant cohomology is determined by the fixed points of codimension 1 subtori. Especially, when the fixed points of the torus are finite and fixed varieties under the action of codimension 1 subtori have dimension less than or equal to 2, equivariant cohomology can be described by discrete conditions on the pair of fixed points via G...
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We study the equivariant K-group of the affine flag manifold with respect to the Borel group action. We prove that the structure sheaf of the (infinite-dimensional) Schubert variety in the K-group is represented by a unique polynomial, which we call the affine Grothendieck polynomial.
متن کاملLinear Conditions Imposed on Flag Varieties
We study subvarieties of the flag variety called Hessenberg varieties, defined by certain linear conditions. These subvarieties arise naturally in applications including geometric representation theory, number theory, and numerical analysis. We describe completely the homology of Hessenberg varieties over GLn(C) and show that they have no odd-dimensional homology. We provide an explicit geometr...
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We study the Jordan-Hölder series for nearby cycles on certain Shimura varieties and Rapoport-Zink local models, and on finite-dimensional pieces of Beilinson’s deformation of the affine Grassmannian to the affine flag variety (and their p-adic analogues). We give a formula for the multiplicities of irreducible constituents in terms of certain cohomology groups, and we also provide an algorithm...
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Building on the theory of parity sheaves due to Juteau–Mautner– Williamson, we develop a formalism of “mixed modular perverse sheaves” for varieties equipped with a stratification by affine spaces. We then give two applications: (1) a “Koszul-type” derived equivalence relating a given flag variety to the Langlands dual flag variety, and (2) a formality theorem for the modular derived category o...
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