On the Divisibility of Degrees of Representations of Lie Algebras

2023/12/01 by Shah, Varun, Spallone, Steven
#Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2312.00544

Abstract

Let \mathfrak g be a reductive Lie algebra, and m a positive integer. There is a natural density of irreducible representations of \mathfrak g, whose degrees are not divisible by m. For \mathfrak g=\mathfrakgl_n, 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.

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