Mixing of frame flow for rank one locally symmetric spaces and measure classification

Dale Winter

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arXiv · 1403.2425

Mixing of frame flow for rank one locally symmetric spaces and measure classification

Dale Winter

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Abstract

Let $G$ be a connected simple linear Lie group of rank one, and let $\Gamma <G$ be a discrete Zariski dense subgroup admitting a finite Bowen-Margulis-Sullivan measure $m^{\operatorname{BMS}}$. We show that the right translation action of the one dimensional diagonalizable subgroup is mixing on $(\Gamma \backslash G, m^{\operatorname{BMS}})$. Together with the work of Roblin, this proves ergodicity of the Burger-Roblin measure under the horospherical group $N$, establishes a classification theorem for $N$ invariant Radon measures on $\Gamma \backslash G$, and provides precise asymptotics for the Haar measure matrix coefficients.

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Dale Winter. 2014-03-10. Mixing of frame flow for rank one locally symmetric spaces and measure classification. https://arxiv.org/abs/1403.2425

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