Polynomial representation growth and alternating quotients.

12 November 2013
Ben Martin
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 $n$?