Quasi-isometric free group representations into SL_3(R)

TL;DR

This paper investigates the properties of certain free group representations into SL_3(R), focusing on their quasi-isometric nature, stability, and perturbation behavior in higher rank Lie groups.

Contribution

It introduces new insights into non-Anosov quasi-isometric representations and their instability under perturbations in higher rank semi-simple Lie groups.

Findings

Some quasi-isometric representations can be perturbed to become non-quasi-isometric.

Certain representations exhibit instability properties in their action on flag spaces.

The study identifies cases where these representations are not approximated by Anosov representations.

Abstract

We study quasi-isometric representations of finitely generated non-abelian free groups into some higher rank semi-simple Lie groups which are not Anosov, nor approximated by Anosov. We show in some cases that these can be perturbed to be non-quasi-isometric, or to have some instability properties with respect to their action on the flag space.