Elements of finite order in the normalizer of a maximal torus of a semisimple group

Ivan Arzhantsev; Alexey Galt; Alexey Staroletov

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arXiv · 2604.08108

Elements of finite order in the normalizer of a maximal torus of a semisimple group

Ivan Arzhantsev·Alexey Galt·Alexey Staroletov

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Abstract

We prove that the set of elements of a given finite order in the connected component $N_w$ of the normalizer $N_G(T)$ of a maximal torus $T$ of a semisimple group $G$ is either empty or a disjoint union of finitely many irreducible subvarieties $C_i$. The dimension of each $C_i$ equals the dimension of the subspace of fixed vectors for the action of the element $w$ of the Weyl group $W$ corresponding to the component $N_w$. Moreover, each $C_i$ is an orbit of the action of the torus $T$ on the component $N_w$ by conjugation.

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BibTeX RIS

Ivan Arzhantsev, Alexey Galt, Alexey Staroletov. 2026-04-09. Elements of finite order in the normalizer of a maximal torus of a semisimple group. https://arxiv.org/abs/2604.08108

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