Nilpotent centralizers and good filtrations

Abstract

Let $G$ be a connected reductive group over an algebraically closed field $\mathbb{k}$. Under mild restrictions on the characteristic of $\mathbb{k}$, we show that any $G$-module with a good filtration also has a good filtration as a module for the reductive part of the centralizer of a nilpotent element $x$ in its Lie algebra.

14 pages, 7 tables