Gradings of positive rank on simple Lie algebras

TL;DR

This paper completes the classification of positive rank gradings on simple Lie algebras over algebraically closed fields, determines the associated little Weyl groups, and proves Popov's conjecture on Kostant sections.

Contribution

It provides a comprehensive classification of positive rank gradings, identifies the little Weyl groups, and confirms Popov's conjecture for simple Lie algebras.

Findings

Complete classification of positive rank gradings

Determination of little Weyl groups for each case

Proof of Popov's conjecture on Kostant sections

Abstract

We complete the classification of positive rank gradings on Lie algebras of simple algebraic groups over an algebraically closed field k whose characteristic is zero or not too small, and we determine the little Weyl groups in each case. We also classify the stable gradings and prove Popov's conjecture on the existence of a Kostant section.