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Translate of horospheres and counting problems
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 136, Number 5, October 2014
- pp. 1301-1346
- 10.1353/ajm.2014.0037
- Article
- Additional Information
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Let $G$ be a semisimple Lie group without compact factors, $\Gamma$ be an irreducible lattice in $G$.
In the first part of the article we give the necessary and sufficient condition under which a sequence
of translates of probability ``horospherical measures'' is convergent. And the limiting measure is also
determined when it is convergent (see Theorems~1 and~2 for the precise statements). In the second part,
two applications are presented. The first one is of geometric nature and the second one gives an
alternative way to count the number of rational points on a flag variety.