Invariant Measures for Horospherical Actions and Anosov Groups

By Minju M. Lee, H. Oh. International mathematics research notices, 2020

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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 $\Gamma \backslash G$, 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 that normalizes $N$. One of the main ingredients is to establish the $NM$-ergodicity of all Burger–Roblin measures.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e8ca4c71c79617a52ed5e05336c82439b526ac7d

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Anosov groups: local mixing, counting and equidistribution (2020, background): “We also refer to [30] and [31] where ergodic properties of these measures are discussed.”