PreprintarXiv licencearXiv
Non Uniform Kazhdan Constant for Linear Groups
Abstract
A group Γ generated by a finite set S has Property (T) if the associated Kazhdan constant κ(Γ,S) is positive. If so, the same holds for every finite generating set S. There are Property (T) groups which are uniformly (T), and others which are not. It is a well-known problem whether the classical examples of Property (T) groups, SLn(ℤ), n≥ 3, are uniformly (T) or not. We show that they are not. Moreover, the same holds for every infinite finitely generated linear group.
Related
- Small Kazhdan constants for small generating sets of linear groups
- Higher Kazhdan projections for one relator groups
- Higher Brin--Thompson groups are Kazhdan
- Uniform asymptotics and the Weil--Petersson constant
- Randomly shifted lattice rules for SDEs with constant diffusion: error bounds uniform in time discretization and dimension
BibTeX
@misc{lubotzky2026uniform,
title = {{Non Uniform Kazhdan Constant for Linear Groups}},
author = {Alexander Lubotzky and Jvbin Yao},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.03561},
eprint = {2608.03561},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.03561},
}
RIS
TY - UNPB
TI - Non Uniform Kazhdan Constant for Linear Groups
AU - Alexander Lubotzky
AU - Jvbin Yao
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.03561
UR - https://arxiv.org/abs/2608.03561
AB - A group Γ generated by a finite set S has Property (T) if the associated Kazhdan constant κ(Γ,S) is positive. If so, the same holds for every finite generating set S. There are Property (T) groups which are uniformly (T), and others which are not. It is a well-known problem whether the classical examples of Property (T) groups, SL_n(ℤ), n≥ 3, are uniformly (T) or not. We show that they are not. Moreover, the same holds for every infinite finitely generated linear group.
ER -