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arXiv · 2006.01909

SL($n$) contravariant vector valuations

Jin Li·Dan Ma·Wei Wang
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Abstract

All SL($n$) contravariant vector valuations on polytopes in $\mathbb R^n$ are completely classified without any additional assumptions. The facet vector is defined. It turns out to be the unique such valuation for $n\geq3$. In dimension two, the classification corresponds to the case of SL(2) covariant valuations.

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Jin Li, Dan Ma, Wei Wang. 2020-06-02. SL($n$) contravariant vector valuations. https://arxiv.org/abs/2006.01909

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