Parameterizing Conjugacy Classes of Unramified Tori via Bruhat-Tits Theory
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866910602758193152 |
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| author | DeBacker, Stephen |
| author_facet | DeBacker, Stephen |
| contents | Suppose $k$ is a nonarchimedean local field, $K$ is a maximally unramified extension of $k$, and $\mathbf{G}$ is a connected reductive $k$-group. In this paper we provide parameterizations via Bruhat-Tits theory of: the rational conjugacy classes of $k$-tori in $\mathbf{G}$ that split over $K$; the rational and stable conjugacy classes of the $K$-split components of the centers of unramified twisted Levi subgroups of $\mathbf{G}$; and the rational conjugacy classes of unramified twisted generalized Levi subgroups of $\mathbf{G}$. We also provide parameterizations of analogous objects for finite groups of Lie type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_08389 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Parameterizing Conjugacy Classes of Unramified Tori via Bruhat-Tits Theory DeBacker, Stephen Representation Theory Group Theory Primary 20G25, Secondary 22E35 Suppose $k$ is a nonarchimedean local field, $K$ is a maximally unramified extension of $k$, and $\mathbf{G}$ is a connected reductive $k$-group. In this paper we provide parameterizations via Bruhat-Tits theory of: the rational conjugacy classes of $k$-tori in $\mathbf{G}$ that split over $K$; the rational and stable conjugacy classes of the $K$-split components of the centers of unramified twisted Levi subgroups of $\mathbf{G}$; and the rational conjugacy classes of unramified twisted generalized Levi subgroups of $\mathbf{G}$. We also provide parameterizations of analogous objects for finite groups of Lie type. |
| title | Parameterizing Conjugacy Classes of Unramified Tori via Bruhat-Tits Theory |
| topic | Representation Theory Group Theory Primary 20G25, Secondary 22E35 |
| url | https://arxiv.org/abs/2209.08389 |