Homogeneous asymptotic limits of haar measures of semisimple linear groups and their lattices

Details Homogeneous asymptotic limits of haar measures of semisimple linear groups and their lattices Homogeneous asymptotic limits of haar measures of semisimple linear groups and their lattices

2005-12-12

arxiv.org/abs/math/0512240v2

Mathematics

Representation Theory

Scientific paper

We show that Haar measures of connected semisimple groups, embedded via a representation into a matrix space, have a homogeneous asymptotic limit when viewed from far away and appropriately rescaled. This is still true if the Haar measure of the semisimple group is replaced by the Haar measure of a irreducible lattice of the group, and the asymptotic measure is the same. In the case of an almost simple group of rank greater than 2, a remainder term in obtained. This extends and precises anterior results of Duke, Rudnick and Sarnak, and Eskin-McMullen in the case of a group variety.

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