Year: 2026
Type: preprint
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, $\mathrm{SL}_n(\mathbb{Z})$, $n\geq 3$, are uniformly $(T)$ or not. We show that they are not. Moreover, the same holds for every infinite finitely generated linear group.
Source: arXiv (Cornell University)
Authors: Lubotzky, Alexander, Yao, Jvbin
Institution: East China Normal University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7172486819