# Sheaves on a loop group and langlands duality

@article{Ginzburg1990SheavesOA, title={Sheaves on a loop group and langlands duality}, author={Victor Ginzburg}, journal={Functional Analysis and Its Applications}, year={1990}, volume={24}, pages={326-327} }

An intrinsic construction of the tensor category of finite dimensional representations of the Langlands dual group of G in terms of a tensor category of perverse sheaves on the loop group, LG, is given. The construction is applied to the study of the topology of the affine Grassmannian of G and to establishing a Langlands type correspondence for "automorphic" sheaves on the moduli space of G-bundles.

## 212 Citations

Perverse sheaves on affine flags and langlands dual group

- Mathematics
- 2002

This is the first in a series of papers devoted to describing the category of sheaves on the affine flag manifold of a simple algebraic group in terms of the Langlands dual group. In the present…

Twisted Whittaker model and factorizable sheaves

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- 2009

Let K be a connected compact Lie group, and G its complexification.
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- 2000

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In this paper we provide, under some mild explicit assumptions, a geometric description of the category of representations of the centralizer of a regular unipotent element in a reductive algebraic…

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Let G^v be a complex simple algebraic group. We describe certain morphisms
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Gr of G^v in terms of certain morphisms of…

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- 1997

The purpose of this note is to present a short elementary proof of a theorem due to Faltings and Laumon, saying that the global nilpotent cone is a Lagrangian substack in the cotangent bundle of the…

DIFFERENTIAL OPERATORS ON $G/U$ AND THE AFFINE GRASSMANNIAN

- MathematicsJournal of the Institute of Mathematics of Jussieu
- 2014

We describe the equivariant cohomology of cofibers of spherical perverse sheaves on the affine Grassmannian of a reductive algebraic group in terms of the geometry of the Langlands dual group. In…

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