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- Title
TRANSLATE OF HOROSPHERES AND COUNTING PROBLEMS.
- Authors
MOHAMMADI, AMIR; GOLSEFIDY, ALIREZA SALEHI
- Abstract
Let G be a semisimple Lie group without compact factors, Γ 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.
- Subjects
LIE groups; LIE algebras; SEMISIMPLE Lie groups; GEOMETRY; LATTICE theory
- Publication
American Journal of Mathematics, 2014, Vol 136, Issue 5, p1301
- ISSN
0002-9327
- Publication type
Article
- DOI
10.1353/ajm.2014.0037