For a group and a positive real number , define to be the number of integers less than which are dimensions of irreducible complex representations of . We study the asymptotics of for algebraic groups, arithmetic groups and finitely generated linear groups. In particular we prove an "alternative" for finitely generated linear groups in characteristic zero, showing that either there exists such that for all large , or is virtually abelian (in which case is bounded).
Cite this article
Martin W. Liebeck, Aner Shalev, Dan Segal, The density of representation degrees. J. Eur. Math. Soc. 14 (2012), no. 5, pp. 1519–1537DOI 10.4171/JEMS/339