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

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

2002-01-27

arxiv.org/abs/math/0201256v4

Mathematics

Representation Theory

This is a continuation of math.RT/0201073. 13 pages; some corrections

Scientific paper

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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