Convergence of measures on compactifications of locally symmetric spaces

Daw, C., Gorodnik, A. and Ullmo, E. (2020) Convergence of measures on compactifications of locally symmetric spaces. Mathematische Zeitschrift. ISSN 0025-5874

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To link to this item DOI: 10.1007/s00209-020-02558-w

Abstract/Summary

We conjecture that the set of homogeneous probability measures on the maximal Satake compactification of an arithmetic locally symmetric space $S=\Gamma\backslash G/K$ is compact. More precisely, given a sequence of homogeneous probability measures on $S$, we expect that any weak limit is homogeneous with support contained in precisely one of the boundary components (including $S$ itself). We introduce several tools to study this conjecture and we prove it in a number of cases, including when $G={\rm SL}_3(\mathbb{R})$ and $\Gamma={\rm SL}_3(\mathbb{Z})$.

Item Type: Article Yes Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics 90540 Springer