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arXiv · 1003.3064

Low Degree Representations of Simple Lie Groups

Robert Guralnick·Michael Larsen·Corey Manack
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Abstract

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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Robert Guralnick, Michael Larsen, Corey Manack. 2010-03-16. Low Degree Representations of Simple Lie Groups. https://arxiv.org/abs/1003.3064

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