Representation growth and representation zeta functions of groups

TL;DR

This paper introduces the concepts of representation growth and zeta functions of groups, emphasizing their relevance to arithmetic groups in semisimple algebraic groups, and discusses recent collaborative results without proofs.

Contribution

It provides an overview of key results in representation growth and zeta functions, highlighting recent advances in the context of arithmetic groups.

Findings

Results relevant to arithmetic groups in semisimple algebraic groups

Recent joint work with Avni, Onn, and Voll

Focus on representation growth and zeta functions

Abstract

We give a short introduction to the subject of representation growth and representation zeta functions of groups, omitting all proofs. Our focus is on results which are relevant to the study of arithmetic groups in semisimple algebraic groups, such as the special linear group of degree n over the ring of integers. In the last two sections we state several results which were recently obtained in joint work with N. Avni, U. Onn and C. Voll.