A Langlands dual realization of coherent sheaves on the nilpotent cone

2023/10/16 by Chen, Harrison, Dhillon, Gurbir · 1 citation
#14D24 #Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2310.10539

Abstract

Let G and \checkG be Langlands dual connected reductive groups. We establish a monoidal equivalence of ∞-categories between equivariant quasicoherent sheaves on the formal neighborhood of the nilpotent cone in G and Steinberg-Whittaker D-modules on the loop group of \checkG, as conjectured by Bezrukavnikov. More generally, we establish equivalences between various spectral and automorphic realizations of affine Hecke categories and their modules, confirming conjectures of Bezrukavnikov.

Cited by

• The Parabolic K-motivic Hecke Category

Related

• Perverse sheaves on affine flags and nilpotent cone of the Langlands dual group
• The universal monodromic Arkhipov--Bezrukavnikov equivalence
• On two modular geometric realizations of an affine Hecke algebra
• Constructible sheaves on affine Grassmannians and geometry of the dual nilpotent cone
• Perverse coherent sheaves on the nilpotent cone in good characteristic