Tessellations of an affine apartment by affine weight polytopes
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909391585804288 |
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| author | Bravo, Claudio Hébert, Auguste Izquierdo, Diego Loisel, Benoit |
| author_facet | Bravo, Claudio Hébert, Auguste Izquierdo, Diego Loisel, Benoit |
| contents | Let $\A$ be a finite dimensional vector space and $Φ$ be a finite root system in $\A$. To this data is associated an affine poly-simplicial complex. Motivated by a forthcoming construction of connectified higher buildings, we study "affine weight polytopes" associated to these data. We prove that these polytopes tesselate $\A$. We also prove a kind of "mixed" tessellation, involving the affine weight polytopes and the poly-simplical structure on $\A$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_10282 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tessellations of an affine apartment by affine weight polytopes Bravo, Claudio Hébert, Auguste Izquierdo, Diego Loisel, Benoit Group Theory 20F55 (Primary), 51M20, 20E42 Let $\A$ be a finite dimensional vector space and $Φ$ be a finite root system in $\A$. To this data is associated an affine poly-simplicial complex. Motivated by a forthcoming construction of connectified higher buildings, we study "affine weight polytopes" associated to these data. We prove that these polytopes tesselate $\A$. We also prove a kind of "mixed" tessellation, involving the affine weight polytopes and the poly-simplical structure on $\A$. |
| title | Tessellations of an affine apartment by affine weight polytopes |
| topic | Group Theory 20F55 (Primary), 51M20, 20E42 |
| url | https://arxiv.org/abs/2411.10282 |