Affine braid group actions on derived categories of Springer resolutions

Details Affine braid group actions on derived categories of Springer resolutions Affine braid group actions on derived categories of Springer resolutions

2011-01-19

arxiv.org/abs/1101.3702v2

Mathematics

Representation Theory

68 pages; very minor modifications

Scientific paper

In this paper we construct and study an action of the affine braid group associated to a semi-simple algebraic group on derived categories of coherent sheaves on various varieties related to the Springer resolution of the nilpotent cone. In particular, we describe explicitly the action of the Artin braid group. This action is a "categorical version" of Kazhdan--Lusztig--Ginzburg's construction of the affine Hecke algebra, and is used in particular by the first author and Ivan Mirkovic in the course of the proof of Lusztig's conjectures on equivariant K-theory of Springer fibers.

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