Equivariant Coherent Sheaves, Soergel Bimodules, and Categorification of Affine Hecke Algebras

Details Equivariant Coherent Sheaves, Soergel Bimodules, and Categorification of Affine Hecke Algebras Equivariant Coherent Sheaves, Soergel Bimodules, and Categorification of Affine Hecke Algebras

2011-08-19

arxiv.org/abs/1108.4028v1

Mathematics

Algebraic Geometry

Scientific paper

We give a description of certain categories of equivariant coherent sheaves on Grothendieck's resolution in terms of the categorical affine Hecke algebra of Soergel. As an application, we deduce a relationship of these coherent sheaf categories to the categories of perverse sheaves considered in the work of Bezrukavnikov-Yun, generalizing results of Arkhipov-Bezrukavnikov. In addition, we deduce that the weak braid group action on sheaves of Riche and Bezrukavnikov-Riche can be upgraded to a strict braid group action.

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