On Kazhdan's property (T) for isotropic reductive groups

TL;DR

This paper proves that elementary isotropic reductive groups over certain rings have a Kazhdan subset, extending previous results to a broader class of algebraic groups.

Contribution

It generalizes known Kazhdan property (T) results from Chevalley groups to elementary isotropic reductive groups over finitely generated rings.

Findings

Elementary generators form a Kazhdan subset

Extends Kazhdan property (T) to new class of groups

Generalizes prior results for Chevalley groups

Abstract

We show that the standard set of elementary generators of an elementary isotropic reductive group over a connected finitely generated ring is a Kazhdan subset. This generalizes the corresponding result of M. Ershov, A. Jaikin-Zapirain, and M. Kassabov for Chevalley and twisted Chevalley groups.