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Proceedings Trends in Mathematics Year : 2022

A topological approach to Soergel theory

Abstract

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.
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hal-01846873 , version 1 (23-07-2018)

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Roman Bezrukavnikov, Simon Riche. A topological approach to Soergel theory. Trends in Mathematics, Birkhäuser/Springer, pp.267-343, 2022, Representation theory and algebraic geometry—a conference celebrating the birthdays of Sasha Beilinson and Victor Ginzburg. ⟨hal-01846873⟩
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