The density of representation degrees

Martin W. Liebeck*, Dan Segal, Aner Shalev

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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 α > 0 such that d G(x) > x α for all large x, or G is virtually abelian (in which case d G(x) is bounded).

Original languageAmerican English
Pages (from-to)1519-1537
Number of pages19
JournalJournal of the European Mathematical Society
Issue number5
StatePublished - 2012


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