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Perverse sheaves on affine flags and nilpotent cone of the Langlands dual group

Roman Bezrukavnikov
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Abstract

In math.RT/0201073 we constructed an equivalence between the derived category of equivariant coherent sheaves on the cotangent bundle to the flag variety of a simple algebraic group and a (quotient of) the category of constructible sheaves on the affine flag variety of the Langlands dual group. Below we prove certain properties of this equivalence; provide a similar ``Langlands dual'' description for the category of equivariant coherent sheaves on the nilpotent cone; and deduce some conjectures by Lusztig and Ostrik.

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Roman Bezrukavnikov. 2007-09-04. Perverse sheaves on affine flags and nilpotent cone of the Langlands dual group. https://arxiv.org/abs/math/0201256

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