The sparsity of dimensions of irreducible representations of finite simple groups

Martin W. Liebeck, Aner Shalev

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We show that the set of natural numbers which are dimensions of irreducible complex representations of finite quasisimple groups (excluding the natural representations of alternating groups) has density zero. We also determine the exact asymptotics for this set, showing that it has (7 + o(1))x/ log x elements less than x. Our tools combine representation theory and number theory. An application to finite subgroups of classical Lie groups is given.

Original languageAmerican English
Pages (from-to)467-472
Number of pages6
JournalBulletin of the London Mathematical Society
Volume39
Issue number3
DOIs
StatePublished - Jun 2007

Bibliographical note

Funding Information:
The second author acknowledges the support of an EPSRC Visiting Fellowship at Imperial College London, and a grant from the Israel Science Foundation.

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