Weights for compact connected Lie groups

Abstract

Let ℓ be a prime. If 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 G, we show that the number of weights of the ℓ-fusion system of 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.