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Equivariant Coherent Sheaves, Soergel Bimodules, and Categorification of Affine Hecke Algebras (1108.4028v1)
Published 19 Aug 2011 in math.AG and math.RT
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.