The sparsity of dimensions of irreducible representations of finite simple groups

Martin W. Liebeck; Aner Shalev

doi:10.1112/blms/bdm028

The sparsity of dimensions of irreducible representations of finite simple groups

Martin W. Liebeck, Aner Shalev

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

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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 language	English
Pages (from-to)	467-472
Number of pages	6
Journal	Bulletin of the London Mathematical Society
Volume	39
Issue number	3
DOIs	https://doi.org/10.1112/blms/bdm028
State	Published - 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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10.1112/blms/bdm028

Cite this

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The sparsity of dimensions of irreducible representations of finite simple groups

Abstract

Bibliographical note

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