2024/09/26 by Tom Gannon, Victor Ginzburg, Gannon, Tom +1 · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2409.18054
openalex publication_date 2024/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The group scheme of universal centralizers of a complex reductive group G has a quantization called the spherical nil-DAHA. The category of modules over this ring is equivalent, as a symmetric monoidal category, to the category of bi-Whittaker D-modules on G. We construct a braided monoidal equivalence, called the Knop-Ngô functor, of this category with a full monoidal subcategory of the abelian category of Ad(G)-equivariant D-modules, establishing a D-module abelian counterpart of an equivalence established by Bezrukavnikov and Deshpande, in a different way. As an application of our methods, we prove conjectures of Ben-Zvi and Gunningham by relating this equivalence to parabolic induction and prove a conjecture of Braverman and Kazhdan in the D-module setting.