Elements of finite order in the normalizer of a maximal torus of a semisimple group
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915927030759424 |
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| author | Arzhantsev, Ivan Galt, Alexey Staroletov, Alexey |
| author_facet | Arzhantsev, Ivan Galt, Alexey Staroletov, Alexey |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_08108 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Elements of finite order in the normalizer of a maximal torus of a semisimple group Arzhantsev, Ivan Galt, Alexey Staroletov, Alexey Group Theory Primary 20G07, Secondary 05A05, 15A18, 20F55 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. |
| title | Elements of finite order in the normalizer of a maximal torus of a semisimple group |
| topic | Group Theory Primary 20G07, Secondary 05A05, 15A18, 20F55 |
| url | https://arxiv.org/abs/2604.08108 |