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

2018/01/26 by Judit Abardia-Evéquoz, Abardia-Evéquoz, Judit, Károly J. Böröczky +3 · 1 citation
Physics and Astronomy · Mathematics · #Advanced Differential Geometry Research #Tensor decomposition and applications #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.1801.08680

Abstract

The space of continuous, \rm SL(m,C)-equivariant, m≥ 2, and translation covariant valuations taking values in the space of real symmetric tensors on C^m≅ R^2m of rank r≥ 0 is completely described. The classification involves the moment tensor valuation for r≥ 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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