Simple root flows for Hitchin representations

TL;DR

This paper investigates simple root flows and Liouville currents in Hitchin representations, establishing connections between entropy measures, volume rigidity, and introducing a pressure metric on the Hitchin component.

Contribution

It introduces a new Liouville pressure metric and links Liouville currents to entropy measures in Hitchin representations.

Findings

Liouville current corresponds to the measure of maximal entropy.

Established a Liouville volume rigidity result.

Constructed a Liouville pressure metric on the Hitchin component.

Abstract

We study simple root flows and Liouville currents for Hitchin representations. We show that the Liouville current is associated to the measure of maximal entropy for a simple root flow, derive a Liouville volume rigidity result, and construct a Liouville pressure metric on the Hitchin component.