Discrete Coxeter groups

TL;DR

This survey explores how Coxeter groups, generated by involutions, are used to construct discrete subgroups of Lie groups, highlighting their significance across various mathematical fields.

Contribution

It provides a comprehensive overview of the application of Coxeter groups in constructing discrete subgroups of Lie groups, emphasizing their mathematical importance.

Findings

Coxeter groups are generated by involutions.

They are instrumental in constructing discrete subgroups of Lie groups.

The survey highlights their roles across different areas of mathematics.

Abstract

Coxeter groups are a special class of groups generated by involutions. They play important roles in the various areas of mathematics. This survey particularly focuses on how one uses Coxeter groups to construct interesting examples of discrete subgroups of Lie groups.