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arXiv · 1309.2352

Translate of horospheres and counting problems

Amir Mohammadi·Alireza Salehi Golsefidy
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Abstract

Let G be a semisimple Lie group without compact factors, Γbe 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.

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Amir Mohammadi, Alireza Salehi Golsefidy. 2013-09-10. Translate of horospheres and counting problems. https://arxiv.org/abs/1309.2352

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