Invariant Measures for Horospherical Actions and Anosov Groups

DOI10.1093/IMRN/RNAC262arXiv2008.05296OpenAlexW3048385904MaRDI QIDQ6142314

Hee Oh, Minju Lee

Publication date: 25 January 2024

Published in: (Search for Journal in Brave)

Abstract: Let $Gamma$ be a Zariski dense Anosov subgroup of a connected semisimple real algebraic group $G$. For a maximal horospherical subgroup $N$ of $G$, we show that the space of all non-trivial $NM$-invariant ergodic and $A$-quasi-invariant Radon measures on $$, up to proportionality, is homeomorphic to ${mathbbR}^{extrank,G-1}$, where $A$ is a maximal real split torus and $M$ is a maximal compact subgroup which normalizes $N$. One of the main ingredients is to establish the $NM$-ergodicity of all Burger-Roblin measures.

Full work available at URL: https://arxiv.org/abs/2008.05296

Mathematics Subject Classification ID

Discrete subgroups of Lie groups (22E40) Dynamical systems and ergodic theory (37-XX) Algebraic groups (14Lxx)

Related Items (4)

Hitchin representations of Fuchsian groups ⋮ Ergodic decompositions of geometric measures on Anosov homogeneous spaces ⋮ Conformal measure rigidity for representations via self-joinings ⋮ Patterson-Sullivan measures for transverse subgroups

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