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Translates of homogeneous measures associated with observable subgroups on some homogeneous spaces.
- Source :
-
Compositio Mathematica . Dec2021, Vol. 157 Issue 12, p2657-2698. 42p. - Publication Year :
- 2021
-
Abstract
- In the present article, we study the following problem. Let $\boldsymbol {G}$ be a linear algebraic group over $\mathbb {Q}$ , let $\Gamma$ be an arithmetic lattice, and let $\boldsymbol {H}$ be an observable $\mathbb {Q}$ -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 $(g_n)_*\mu _H$ under the weak- $*$ topology. In the non-divergent case, we give a rather complete classification. We further supplement this by giving a criterion of non-divergence and prove non-divergence for arbitrary sequence $(g_n)$ for certain large $\boldsymbol {H}$. We also discuss some examples and applications of our result. This work can be viewed as a natural extension of the work of Eskin–Mozes–Shah and Shapira–Zheng. [ABSTRACT FROM AUTHOR]
- Subjects :
- *LINEAR algebraic groups
*HOMOGENEOUS spaces
*ARITHMETIC
Subjects
Details
- Language :
- English
- ISSN :
- 0010437X
- Volume :
- 157
- Issue :
- 12
- Database :
- Academic Search Index
- Journal :
- Compositio Mathematica
- Publication Type :
- Academic Journal
- Accession number :
- 154739574
- Full Text :
- https://doi.org/10.1112/S0010437X21007624