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arXiv · 1909.02666

Translates of homogeneous measures associated with observable subgroups on some homogeneous spaces

Runlin Zhang
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Abstract

In the present article we study the following problem. Let G be a linear algebraic group over Q, $\Gamma$ be an arithmetic lattice and H be an observable Q-subgroup. There is a H-invariant measure $\mu_H$ supported on the closed submanifold $H\Gamma/\Gamma$. Given a sequence $g_n$ in G we study the limiting behavior of $(g_n)_*\mu_H$. In the non-divergent case we give a rather complete classification. We further supplement this by giving criterion of non-divergence and prove non-divergence for arbitrary sequence $g_n$ for certain H. This work can be viewed as a natural extension of the work of Eskin--Mozes--Shah and Shapira--Zheng.

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Runlin Zhang. 2019-09-05. Translates of homogeneous measures associated with observable subgroups on some homogeneous spaces. https://arxiv.org/abs/1909.02666

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