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arXiv · 2008.05296

Invariant measures for horospherical actions and Anosov groups

Minju Lee·Hee Oh
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Abstract

Let $Γ$ 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 $Γ\backslash G$, up to proportionality, is homeomorphic to ${\mathbb R}^{\text{rank}\,G-1}$, 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.

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Minju Lee, Hee Oh. 2022-09-20. Invariant measures for horospherical actions and Anosov groups. https://arxiv.org/abs/2008.05296

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