Kostant section, universal centralizer, and a modular derived Satake equivalence

TL;DR

This paper extends Kostant's classical results on the universal centralizer to positive characteristic and integral settings, and applies these to develop a modular derived Satake equivalence, broadening the scope of geometric representation theory.

Contribution

It introduces analogues of Kostant's results in positive characteristic and integral contexts, enabling a modular version of the derived Satake equivalence.

Findings

Established Kostant-type results in positive characteristic

Developed a modular derived Satake equivalence

Bridged classical and modular representation theories

Abstract

We prove analogues of fundamental results of Kostant on the universal centralizer of a connected reductive algebraic group for algebraically closed fields of positive characteristic (with mild assumptions), and for integral coefficients. As an application, we use these results to obtain a "mixed modular" analogue of the derived Satake equivalence of Bezrukavnikov-Finkelberg.