12 November 2013

17:00

Ben Martin

Abstract

Let $\Gamma$ be a group and let $r_n(\Gamma)$ denote the
number of isomorphism classes of irreducible $n$-dimensional complex
characters of $\Gamma$. Representation growth is the study of the
behaviour of the numbers $r_n(\Gamma)$. I will give a brief overview of
representation growth.
We say $\Gamma$ has polynomial representation growth if $r_n(\Gamma)$ is
bounded by a polynomial in $n$. I will discuss a question posed by
Brent Everitt: can a group with polynomial representation growth have
the alternating group $A_n$ as a quotient for infinitely many $n$?