Determination of the structure of algebraic curvature tensors by means of Young symmetrizers
<|reference_start|>Determination of the structure of algebraic curvature tensors by means of Young symmetrizers: For a positive definite fundamental tensor all known examples of Osserman algebraic curvature tensors have a typical structure. They can be produced from a metric tensor and a finite set of skew-symmetric matrices which fulfil Clifford commutation relations. We show by means of Young symmetrizers and a theorem of S. A. Fulling, R. C. King, B. G. Wybourne and C. J. Cummins that every algebraic curvature tensor has a structure which is very similar to that of the above Osserman curvature tensors. We verify our results by means of the Littlewood-Richardson rule and plethysms. For certain symbolic calculations we used the Mathematica packages MathTensor, Ricci and PERMS.<|reference_end|>
@article{fiedler2002determination,
    title={Determination of the structure of algebraic curvature tensors by means
  of Young symmetrizers},
    author={B. Fiedler},
    journal={Seminaire Lotharingien de Combinatoire, 48 (2003) Article B48d},
    year={2002},
    archivePrefix={arXiv},
    eprint={math/0212278},
    primaryClass={math.CO cs.SC math.DG}
}