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arXiv · 1801.08680

${\rm SL}(m,C)$-equivariant and translation covariant continuous tensor valuations

Judit Abardia-Evéquoz·Károly J. Böröczky·Mátyás Domokos·Dávid Kertész
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Abstract

The space of continuous, ${\rm SL}(m,C)$-equivariant, $m\geq 2$, and translation covariant valuations taking values in the space of real symmetric tensors on $C^m\cong R^{2m}$ of rank $r\geq 0$ is completely described. The classification involves the moment tensor valuation for $r\geq 1$ and is analogous to the classification of the corresponding tensor valuations that are ${\rm SL}(2m,R)$-equivariant, although the method of proof cannot be adapted.

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Judit Abardia-Evéquoz, Károly J. Böröczky, Mátyás Domokos, Dávid Kertész. 2018-01-26. ${\rm SL}(m,C)$-equivariant and translation covariant continuous tensor valuations. https://arxiv.org/abs/1801.08680

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