Moment map flow on real reductive Lie groups and GIT estimates

TL;DR

This paper explores the properties of the moment map and stratification in real reductive Lie groups, providing algebraic insights and extending the understanding of geometric invariant theory in this context.

Contribution

It offers a functorial, algebraic perspective on the moment map, stratification, and their properties in real reductive Lie groups, expanding prior geometric approaches.

Findings

Analysis of moment map properties in real reductive groups

Development of algebraic and functorial frameworks for stratification

Connections to geometric invariant theory estimates

Abstract

A finite dimensional real vector space carrying an action of a real reductive group possesses a moment map and a stratification as defined by Kirwan and Ness. In this article we investigate the properties of the moment map, the Kirwan-Ness stratification, and Lauret's application from a more functorial, algebraic point of view.