Anosov representations acting on homogeneous spaces: domains of discontinuity

TL;DR

This paper constructs maximal open domains of discontinuity for Anosov representations acting on various homogeneous spaces, extending previous work and providing new insights into their geometric and dynamical properties.

Contribution

It generalizes existing constructions of discontinuity domains for Anosov representations to broader homogeneous spaces, including symmetric spaces, and identifies the largest such domains.

Findings

Constructed open domains of discontinuity for Anosov representations.

Extended previous work to include symmetric and pseudo-Riemannian spaces.

Identified maximal domains for Zariski dense Anosov representations.

Abstract

We construct open domains of discontinuity for Anosov representations acting on some homogeneous spaces, including (pseudo-Riemannian) symmetric spaces. This generalizes work of Kapovich-Leeb-Porti on flag spaces. Our results complement those of Gu\'eritaud-Guichard-Kassel-Wienhard, who constructed proper actions of Anosov representations. For Zariski dense Anosov representations with respect to a minimal parabolic subgroup acting on some symmetric spaces, we show that our construction describes the largest possible open domains of discontinuity.