Property (T) for groups acting on affine buildings

TL;DR

This paper proves that groups acting geometrically on thick affine buildings possess property (T), providing a broader criterion for property (T) applicable to groups acting on partite complexes.

Contribution

It establishes property (T) for groups acting on affine buildings and introduces a general criterion for property (T) in groups acting on partite complexes.

Findings

Groups acting on thick affine buildings have property (T)

A general criterion for property (T) for groups acting on partite complexes

Extension of property (T) results to broader classes of groups

Abstract

We prove that a group acting geometrically on a thick affine building has property (T). A more general criterion for property (T) is given for groups acting on partite complexes.