SL(𝑛) covariant vector valuations on polytopes

Zeng, Chunna; Ma, Dan

doi:10.1090/tran/7468

SL($\textbf {\textit {n}}$) covariant vector valuations on polytopes
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by Chunna Zeng and Dan Ma PDF

Trans. Amer. Math. Soc. 370 (2018), 8999-9023 Request permission

Abstract:

All $\mathrm {SL}(n)$ covariant vector valuations on convex polytopes in $\mathbb {R}^n$ are completely classified without any continuity assumptions. The moment vector turns out to be the only such valuation if $n\ge 3$, while two new functionals show up in dimension two.

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