SLn Equivariant Matrix-Valued Valuations on Polytopes-Reference-Cited by-同舟云学术

SLn Equivariant Matrix-Valued Valuations on Polytopes

Published:2021-10-13 Issue: Volume: Page:
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Wang Wei¹

Affiliation:

1. School of Mathematics and Computational Science, Hunan University of Science and Technology, Xiangtan, 411201, P.R. China

Abstract

Abstract All $\textrm{SL}(n)$ equivariant matrix-valued valuations on polytopes in $\mathbb{R}^{n}$ are completely classified without any continuity assumptions. Moreover, the symmetry assumption of matrices is removed. The moment matrix is shown to be the only such valuation if $n\geq 4$, while new functionals show up in dimensions two and three.

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

http://academic.oup.com/imrn/advance-article-pdf/doi/10.1093/imrn/rnab290/40632836/rnab290.pdf

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4. Harmonic analysis of translation invariant valuations;Alesker;Geom. Funct. Anal.,2011

5. Mathematical Surveys and Monographs;Artstein-Avidan,2015

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