Simplicity of twin tree lattices with non-trivial commutation relations

TL;DR

This paper establishes a criterion for simplicity in twin tree lattices, specifically applying to rank two Kac-Moody groups over finite fields with non-trivial relations, leading to new examples of simple non-uniform lattices in product of trees.

Contribution

It provides a new simplicity criterion for twin tree lattices, expanding understanding of their structure in the context of Kac-Moody groups over finite fields.

Findings

Proves a simplicity criterion for certain twin tree lattices

Identifies simple non-uniform lattices in products of two trees

Applies to rank two Kac-Moody groups with non-trivial relations

Abstract

We prove a simplicity criterion for certain twin tree lattices. It applies to all rank two Kac-Moody groups over finite fields with non-trivial commutation relations, thereby yielding examples of simple non-uniform lattices in the product of two trees.