Spectral gap and character limits in arithmetic groups
Group Theory
2024-06-18 v3 Operator Algebras
Abstract
We establish vanishing results for limits of characters in various discrete groups, most notably irreducible lattices in higher rank semisimple Lie groups. As an application, we show that any sequence of finite-dimensional representations converges to the regular representation in the Fell topology. We achieve this by studying the geometry of the simplex of traces of discrete groups having Kazhdan's property (T) or its relative generalizations.
Cite
@article{arxiv.2308.05562,
title = {Spectral gap and character limits in arithmetic groups},
author = {Arie Levit and Raz Slutsky and Itamar Vigdorovich},
journal= {arXiv preprint arXiv:2308.05562},
year = {2024}
}
Comments
a rewrite of introduction; minor corrections of inaccuracies of computations in section 4