A topological approach to Soergel theory

Overview & Synopsis

We develop a "Soergel theory" for Bruhat-constructible perverse sheaves on the flag variety G/B of a complex reductive group G, with coefficients in an arbitrary field k. Namely, we describe the endomorphisms of the projective cover of the skyscraper sheaf in terms of a "multiplicative" coinvariant algebra, and then establish an equivalence of categories between projective (or tilting) objects in this category and a certain category of "Soergel modules" over this algebra. We also obtain a description of the derived category of T-monodromic k-sheaves on G/U (where U,T ⊂ B are the unipotent radical and the maximal torus), as a monoidal category.