Weights for compact connected Lie groups

Abstract

Let \(\ell \) be a prime. If \(\textbf{G}\) is a compact connected Lie group, or a connected reductive algebraic group in characteristic different from \(\ell \), and \(\ell \) is a good prime for \(\textbf{G}\), we show that the number of weights of the \(\ell \)-fusion system of \(\textbf{G}\) 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.