Perverse sheaves on affine flags and nilpotent cone of the langlands dual group
By R. Bezrukavnikov. 2002
54 citations recorded by the source corpus.
This paper is a continuation of [2]. In [2], 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) a category of constructible sheaves on the affine flag variety of the Langlands dual group. Below we prove certain properties of this equivalence related to cells in the affineWeyl group; provide a similar “Langlands dual” description for the category of equivariant coherent sheaves on the nilpotent cone, and link it to perverse coherent sheaves; and deduce some conjectures by Lusztig and Ostrik.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/eddccd3de288dd8d8ac2385e841acca78fedc307
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In Algebra and Number Theory
In Geometry and Topology
- R. Bezrukavnikov
- Simon Riche
- Geordie Williamson
- I. Losev
- Arend Bayer
- Alexander Polishchuk
- D. Arinkin
- Sergey V. Arkhipov
In Mathematical Physics
- R. Bezrukavnikov
- I. Losev
- Simon Riche
- Arend Bayer
- Alexander Polishchuk
- Michel van den Bergh
- Geordie Williamson
- D. Arinkin
Citations in the corpus
- On two geometric realizations of an affine Hecke algebra (2012, background): “It has been conjectured by Lusztig and proved in [12] that this order matches the adjacency order on the set of nilpotent orbits under the bijection between two-sided cells and N /Gˇ.”