Kazhdan constants for Chevalley groups over the integers
Group Theory
2024-11-05 v3 Operator Algebras
Abstract
We compute lower bounds for Kazhdan constants of Chevalley groups over the integers, endowed with the standard Steinberg generators. For types other than , these are the first explicit asymptotically sharp such bounds. The method relies on establishing a new connection between the structure of a root system grading a family of groups and the behaviour of the square of the Laplace operator in the family.
Keywords
Cite
@article{arxiv.2306.12358,
title = {Kazhdan constants for Chevalley groups over the integers},
author = {Marek Kaluba and Dawid Kielak},
journal= {arXiv preprint arXiv:2306.12358},
year = {2024}
}
Comments
Referees' comments were incorporated. To appear in Rev. Math. Iberoam