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Low degree representations of simple Lie groups


Authors: Robert Guralnick, Michael Larsen and Corey Manack
Journal: Proc. Amer. Math. Soc. 140 (2012), 1823-1834
MSC (2010): Primary 22C05, 22E46
Published electronically: August 24, 2011
MathSciNet review: 2869167
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Abstract: We show that the number of irreducible representations of degree $ \le n$ of any simple compact Lie group $ G$ is $ \le n$. If the rank of $ G$ is large, the bound is much smaller. A consequence is that the number of conjugacy classes of closed maximal subgroups for a simple compact or complex Lie group of rank $ r$ is $ O(r)$.


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Additional Information

Robert Guralnick
Affiliation: Department of Mathematics, University of Southern California, 3620 South Vermont Avenue, Los Angeles, California 90089-2532
Email: guralnic@usc.edu

Michael Larsen
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
Email: mjlarsen@indiana.edu

Corey Manack
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
Address at time of publication: Department of Mathematics, Amherst College, Amherst, Massachusetts 01002-5000
Email: cmanack1@gmail.com

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-11007-4
Received by editor(s): March 22, 2010
Received by editor(s) in revised form: December 9, 2010, January 4, 2011, and January 13, 2011
Published electronically: August 24, 2011
Additional Notes: The authors were partially supported by NSF Grants DMS-0653873, DMS-1001962 and DMS-0800705.
Communicated by: Gail R. Letzter
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.