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Convergence of measures on compactifications of locally symmetric spaces

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Daw, C. ORCID: https://orcid.org/0000-0002-2488-6729, Gorodnik, A. and Ullmo, E. (2021) Convergence of measures on compactifications of locally symmetric spaces. Mathematische Zeitschrift, 297 (3-4). pp. 1293-1328. 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=Γ∖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=SL3(R) and Γ=SL3(Z).

Item Type:Article
Refereed:Yes
Divisions:Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:90540
Publisher:Springer
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