Dimensions of Newton strata in the adjoint quotient of reductive groups

TL;DR

This paper extends the classical Newton polygon theory to split reductive groups and provides a root-theoretic formula for the dimensions of Newton strata in their adjoint quotients.

Contribution

It generalizes Newton polygon theory from GL(n) to all split reductive groups and introduces a root-theoretic formula for Newton strata dimensions.

Findings

Generalization of Newton polygons to split reductive groups

Root-theoretic formula for Newton strata dimensions

Enhanced understanding of the structure of adjoint quotients

Abstract

This paper generalizes the classical theory of Newton polygons from the case of general linear groups to the case of split reductive groups. It also gives a root-theoretic formula for dimensions of Newton strata in the adjoint quotients of reductive groups.