On Chamber-regular $\tilde C_2$-Lattices
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915612024897536 |
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| author | Stamer, Franziska Mite, Thomas Titz |
| author_facet | Stamer, Franziska Mite, Thomas Titz |
| contents | We construct the first examples of chamber-regular lattices on $\tilde C_2$-buildings. Assuming a conjecture of Kantor our list of examples becomes a classification for chamber-regular $\tilde C_2$-lattices on locally-finite $\tilde C_2$-buildings. The links of special vertices in the buildings we construct, are all isomorphic to (the incidence graph of) the unique generalized quadrangle $Q$ of order (3,5). In particular our constructions involve chamber-regular actions on $Q$. These actions on $Q$ are the first (and if Kantor's conjecture holds the only) chamber-regular actions on a finite generalized quadrangle and therefore interesting in their own right. Moreover $Q$ is not Moufang and therefore none of our examples is a Bruhat-Tits building and all our lattices are exotic building lattices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_08312 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Chamber-regular $\tilde C_2$-Lattices Stamer, Franziska Mite, Thomas Titz Group Theory 20F65, 51E24 We construct the first examples of chamber-regular lattices on $\tilde C_2$-buildings. Assuming a conjecture of Kantor our list of examples becomes a classification for chamber-regular $\tilde C_2$-lattices on locally-finite $\tilde C_2$-buildings. The links of special vertices in the buildings we construct, are all isomorphic to (the incidence graph of) the unique generalized quadrangle $Q$ of order (3,5). In particular our constructions involve chamber-regular actions on $Q$. These actions on $Q$ are the first (and if Kantor's conjecture holds the only) chamber-regular actions on a finite generalized quadrangle and therefore interesting in their own right. Moreover $Q$ is not Moufang and therefore none of our examples is a Bruhat-Tits building and all our lattices are exotic building lattices. |
| title | On Chamber-regular $\tilde C_2$-Lattices |
| topic | Group Theory 20F65, 51E24 |
| url | https://arxiv.org/abs/2511.08312 |