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

2011/08/19 by Christopher Stephen Dodd, Dodd, Christopher · 2 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1108.4028

openalex publication_date 2011/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Modular affine Hecke category and regular centralizer
• Exotic tilting sheaves, parity sheaves on affine Grassmannians, and the Mirkovic-Vilonen conjecture

Related

• Perverse coherent sheaves (after Deligne)
• Affine braid group actions on derived categories of Springer resolutions
• Semiorthogonal decompositions of the categories of equivariant coherent\n sheaves for some reflection groups
• Folding with Soergel bimodules
• Linear structure on a finite Hecke category in type A