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arXiv · 2411.10282

Tessellations of an affine apartment by affine weight polytopes

Claudio Bravo·Auguste Hébert·Diego Izquierdo·Benoit Loisel
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Abstract

Let $\A$ be a finite dimensional vector space and $\Phi$ 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 $\A$.

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Claudio Bravo, Auguste Hébert, Diego Izquierdo, Benoit Loisel. 2024-11-15. Tessellations of an affine apartment by affine weight polytopes. https://arxiv.org/abs/2411.10282

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