Measure rigidity for solvable group actions in the space of lattices

Manfred Einsiedler; Ronggang Shi

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arXiv · 1702.03084

Measure rigidity for solvable group actions in the space of lattices

Manfred Einsiedler·Ronggang Shi

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Abstract

We study invariant probability measures on the homogeneous space $\mathrm{SL}_n(\mathbb R)/\mathrm{SL}_n(\mathbb Z)$ for the action of subgroups of $\mathrm{SL}_n(\mathbb R)$ of the form $SF$ where $F$ is generated by one parameter unipotent groups and $S$ is a one parameter $\mathbb R$-diagonalizable group normalizing $F$. Under the assumption that $S$ contains an element with only one eigenvalue less than one (counted with multiplicity) and others bigger than one we prove that all the $SF$ invariant and ergodic probability measures on $\mathrm{SL}_n(\mathbb R)/\mathrm{SL}_n(\mathbb Z)$ are homogeneous.

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BibTeX RIS

Manfred Einsiedler, Ronggang Shi. 2017-02-10. Measure rigidity for solvable group actions in the space of lattices. https://arxiv.org/abs/1702.03084

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