$Λ$-buildings associated to quasi-split groups over $Λ$-valued fields
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arXiv
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| Formato: | Preprint |
| Publicado: |
2020
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| _version_ | 1866913222468042752 |
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| author | Hébert, Auguste Izquierdo, Diego Loisel, Benoit |
| author_facet | Hébert, Auguste Izquierdo, Diego Loisel, Benoit |
| contents | Let $\mathbf{G}$ be a quasi-split reductive group and $\mathbb{K}$ be a Henselian field equipped with a valuation $ω:\mathbb{K}^{\times}\rightarrow Λ$, where $Λ$ is a non-zero totally ordered abelian group. In 1972, Bruhat and Tits constructed a building on which the group $\mathbf{G}(\mathbb{K})$ acts provided that $Λ$ is a subgroup of $\mathbb{R}$. In this paper, we deal with the general case where there are no assumptions on $Λ$ and we construct a set on which $\mathbf{G}(\mathbb{K})$ acts. We then prove that it is a $Λ$-building, in the sense of Bennett. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2001_01542 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | $Λ$-buildings associated to quasi-split groups over $Λ$-valued fields Hébert, Auguste Izquierdo, Diego Loisel, Benoit Group Theory Metric Geometry Representation Theory 20E42, 51E24, 20G15 Let $\mathbf{G}$ be a quasi-split reductive group and $\mathbb{K}$ be a Henselian field equipped with a valuation $ω:\mathbb{K}^{\times}\rightarrow Λ$, where $Λ$ is a non-zero totally ordered abelian group. In 1972, Bruhat and Tits constructed a building on which the group $\mathbf{G}(\mathbb{K})$ acts provided that $Λ$ is a subgroup of $\mathbb{R}$. In this paper, we deal with the general case where there are no assumptions on $Λ$ and we construct a set on which $\mathbf{G}(\mathbb{K})$ acts. We then prove that it is a $Λ$-building, in the sense of Bennett. |
| title | $Λ$-buildings associated to quasi-split groups over $Λ$-valued fields |
| topic | Group Theory Metric Geometry Representation Theory 20E42, 51E24, 20G15 |
| url | https://arxiv.org/abs/2001.01542 |