Translate of horospheres and counting problems
Dynamical Systems
2013-09-11 v1 Group Theory
Number Theory
Abstract
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.
Keywords
Cite
@article{arxiv.1309.2352,
title = {Translate of horospheres and counting problems},
author = {Amir Mohammadi and Alireza Salehi Golsefidy},
journal= {arXiv preprint arXiv:1309.2352},
year = {2013}
}
Comments
41 pages (12 pt), 3 figures