The density of representation degrees

Liebeck, Martin, Segal, Dan, and Shalev, Aner. "The density of representation degrees." Journal of the European Mathematical Society 014.5 (2012): 1519-1537. <http://eudml.org/doc/277618>.

@article{Liebeck2012,
abstract = {For a group $G$ and a positive real number $x$, define $d_G(x)$ to be the number of integers less than $x$ which are dimensions of irreducible complex representations of $G$. We study the asymptotics of $d_G(x)$ for algebraic groups, arithmetic groups and finitely generated linear groups. In particular we prove an “alternative” for finitely generated linear groups $G$ in characteristic zero, showing that either there exists $\alpha >0$ such that $d_G(x)>x^\{\alpha \}$ for all large $x$, or $G$ is virtually abelian (in which case $d_G(x)$ is bounded).},
author = {Liebeck, Martin, Segal, Dan, Shalev, Aner},
journal = {Journal of the European Mathematical Society},
keywords = {dimensions of irreducible complex representations; representation degrees; complex simple algebraic groups; arithmetic groups; finitely generated linear groups; asymptotics of density functions; virtually Abelian groups; dimensions of irreducible complex representations; representation degrees; complex simple algebraic groups; arithmetic groups; finitely generated linear groups; asymptotics of density functions; virtually Abelian groups},
language = {eng},
number = {5},
pages = {1519-1537},
publisher = {European Mathematical Society Publishing House},
title = {The density of representation degrees},
url = {http://eudml.org/doc/277618},
volume = {014},
year = {2012},
}

TY - JOUR
AU - Liebeck, Martin
AU - Segal, Dan
AU - Shalev, Aner
TI - The density of representation degrees
JO - Journal of the European Mathematical Society
PY - 2012
PB - European Mathematical Society Publishing House
VL - 014
IS - 5
SP - 1519
EP - 1537
AB - For a group $G$ and a positive real number $x$, define $d_G(x)$ to be the number of integers less than $x$ which are dimensions of irreducible complex representations of $G$. We study the asymptotics of $d_G(x)$ for algebraic groups, arithmetic groups and finitely generated linear groups. In particular we prove an “alternative” for finitely generated linear groups $G$ in characteristic zero, showing that either there exists $\alpha >0$ such that $d_G(x)>x^{\alpha }$ for all large $x$, or $G$ is virtually abelian (in which case $d_G(x)$ is bounded).
LA - eng
KW - dimensions of irreducible complex representations; representation degrees; complex simple algebraic groups; arithmetic groups; finitely generated linear groups; asymptotics of density functions; virtually Abelian groups; dimensions of irreducible complex representations; representation degrees; complex simple algebraic groups; arithmetic groups; finitely generated linear groups; asymptotics of density functions; virtually Abelian groups
UR - http://eudml.org/doc/277618
ER -