Abstract
Let G be a connected simple linear Lie group of rank one, and let Γ < G be a discrete Zariski dense subgroup admitting a finite Bowen-Margulis-Sullivan measure m BMS. We show that the right translation action of the one-dimensional diagonalizable subgroup is mixing on (Γ\G, m 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 Γ\G, and provides precise asymptotics for the Haar measure matrix coefficients.
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Winter, D. Mixing of frame flow for rank one locally symmetric spaces and measure classification. Isr. J. Math. 210, 467–507 (2015). https://doi.org/10.1007/s11856-015-1258-5
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DOI: https://doi.org/10.1007/s11856-015-1258-5