2018/07/19 by Roman Bezrukavnikov, Bezrukavnikov, Roman, Simon Riche +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1807.07614
openalex publication_date 2018/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 \Bbbk. 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 \Bbbk-sheaves on G/U (where U, T⊂ B are the unipotent radical and the maximal torus), as a monoidal category, in terms of coherent sheaves on the formal neighborhood of the base point in T^\vee_\Bbbk ×(T^\vee_\Bbbk)W T^\vee_\Bbbk, where T^\vee_\Bbbk is the \Bbbk-torus dual to T.