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

Abstract

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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Cited by in corpus (6)

• Exotic tilting sheaves, parity sheaves on affine Grassmannians, and the Mirkovic-Vilonen conjecture
• Differential operators on G/U and the affine Grassmannian
• Modular affine Hecke category and regular centralizer
• Modular affine Hecke category and regular unipotent centralizer
• Kostant section, universal centralizer, and a modular derived Satake equivalence
• Notes on exotic and perverse-coherent sheaves