Weights for compact connected Lie groups

Abstract

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