Low Degree Representations of Simple Lie Groups

Details Low Degree Representations of Simple Lie Groups Low Degree Representations of Simple Lie Groups

2010-03-16

arxiv.org/abs/1003.3064v1

Mathematics

Representation Theory

15 pages

Scientific paper

We give upper bounds for the number of irreducible representations of dimension at most n for a compact semisimple Lie group. In particular, we prove that there are at most n irreducible representations of dimension at most n for a simple compact Lie group. We use this prove that the number of conjugacy classes of maximal subgroups of a compact simple Lie group is O(r) where r is the Lie rank. We also give a short proof that the dimensions of the weight spaces of a maximal torus are small relative to the dimension of an irreducible module.

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