Irreducible discrete subgroups in products of simple Lie groups

TL;DR

This paper constructs a specific example of an irreducible discrete subgroup in a product of simple Lie groups that is not a lattice, addressing a previously open question.

Contribution

It provides the first known example of an irreducible discrete subgroup in a product of simple Lie groups that is not a lattice.

Findings

Constructed an explicit example in SL(2,R)×SL(2,R)

Answered an open question in the field

Demonstrated existence of non-lattice irreducible discrete subgroups

Abstract

We produce an example of an irreducible discrete subgroup in the product $SL(2,\R)\times SL(2,\R)$ which is not a lattice. This answers a question asked in [15].