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arXiv · 2303.05932

Weights for compact connected Lie groups

Radha Kessar·Gunter Malle·Jason Semeraro
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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.

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Radha Kessar, Gunter Malle, Jason Semeraro. 2023-03-10. Weights for compact connected Lie groups. https://arxiv.org/abs/2303.05932

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