On the divisibility of degrees of representations of Lie groups

Abstract

Let g be a reductive Lie algebra and m a positive integer. There is a natural density of irreducible representations of g, whose degrees are not divisible by m. For g = gln , this density decays exponentially to 0 as n. Similar results hold for simple Lie algebras and Lie groups, and there are versions for self-dual and orthogonal representations.