Low degree representations of simple Lie groups

Guralnick, Robert; Larsen, Michael; Manack, Corey

doi:10.1090/S0002-9939-2011-11007-4

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 $O(r)$.

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