Weights for compact connected Lie groups

Abstract

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