2000 character limit reached
Universal monodromic tilting sheaves
Published 4 May 2023 in math.RT | (2305.03033v6)
Abstract: Let $G$ be a complex adjoint reductive group and $R$ be the group ring of the coweight lattice. We construct the universal monodromic big tilting sheaf on base affine space and show that its endomorphisms are $R \otimes_{RW} R$. Our arguments are self contained, so formal completion implies a short new proof of Soergel's prounipotent endomorphismensatz with arbitrary field coefficients. We give a Soergel bimodules description of the universal monodromic Hecke category and deduce a conjecture of Eberhardt that uncompletes Koszul duality.
- The stack of local systems with restricted variation and geometric Langlands theory with nilpotent singular support. arXiv:2010.01906, 2020.
- Faisceaux pervers. Astérisque, 100(1), 1982.
- Tilting exercises. Moscow Math Journal, pages 547–557, 2004.
- Schubert cells and cohomology of the spaces G/P. Russian Mathematical Surveys, 28(3):1, 1973.
- Koszul duality patterns in representation theory. Journal of the American Mathematical Society, 9(2):473–527, 1996.
- A topological approach to Soergel theory. In Representation Theory and Algebraic Geometry: A Conference Celebrating the Birthdays of Sasha Beilinson and Victor Ginzburg, pages 267–343. Springer, 2021.
- On Koszul duality for Kac-Moody groups. Representation Theory of the American Mathematical Society, 17(1):1–98, 2013.
- Quantum K-theoretic geometric Satake: the SL(n) case. Compositio Mathematica, 154(2):275–327, 2018.
- Jens Niklas Eberhardt. K-theory Soergel bimodules. arXiv:2208.01665, 2022.
- Ben Elias. Quantum Satake in type A. Part I. J. Comb. Algebra, 1(1):63–125, 2017.
- Dennis Gaitsgory. Twisted Whittaker model and factorizable sheaves. Selecta Mathematica, 13:617–659, 2008.
- Equivariant cohomology, Koszul duality, and the localization theorem. Inventiones mathematicae, 131(1):25–84, 1998.
- Sheaves on Manifolds, volume 292 of Grundlehren der mathematischen Wissenschaften. Springer, 1990.
- Hideyuki Matsumura. Commutative algebra, volume 120. WA Benjamin New York, 1970.
- Wolfgang Soergel. Kategorie O, perverse garben und moduln über den koinvarianten zur Weylgruppe. Journal of the American Mathematical Society, 3(2):421–445, 1990.
- Wolfgang Soergel. Kazhdan-Lusztig-polynome und unzerlegbare bimoduln über polynomringen. Journal of the Institute of Mathematics of Jussieu, 6(3):501–525, 2007.
- Robert Steinberg. On a theorem of Pittie. Topology, 14(2):173–177, 1975.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.