Low degree representations of simple Lie groups
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- by Robert Guralnick, Michael Larsen and Corey Manack PDF
- Proc. Amer. Math. Soc. 140 (2012), 1823-1834 Request permission
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 $O(r)$.References
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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
- MR Author ID: 78455
- Email: guralnic@usc.edu
- Michael Larsen
- Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
- MR Author ID: 293592
- 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
- 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
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 140 (2012), 1823-1834
- MSC (2010): Primary 22C05, 22E46
- DOI: https://doi.org/10.1090/S0002-9939-2011-11007-4
- MathSciNet review: 2869167