Low degree representations of simple Lie groups

Source abstract

We show that the number of irreducible representations of degree ≤ n \le n of any simple compact Lie group G G is ≤ n \le n . If the rank of G 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 r is O ( r ) O(r) .