Weights for compact connected Lie groups

2023/03/10 by Kessar, Radha, Malle, Gunter, Semeraro, Jason
#20C20 #55R35 #57T10 #Algebraic Topology (math.AT) #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2303.05932

Abstract

Let ℓ be a prime. If \mathbf G is a compact connected Lie group, or a connected reductive algebraic group in characteristic different from ℓ, and ℓ is a good prime for \mathbf G, we show that the number of weights of the ℓ-fusion system of \mathbf G is equal to the number of irreducible characters of its Weyl group. The proof relies on the classification of ℓ-stubborn subgroups in compact Lie groups.

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