Geodesic
Determination of the Structure of Algebraic Curvature Tensors by Means of Young Symmetrizers
Séminaire lotharingien de combinatoire, Tome 48 (2002-2003)

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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.

Bernd.Fiedler.RoschStr.Leipzig@t-online.de 
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     author = {Bernd Fiedler},
     title = {Determination of the {Structure} of {Algebraic} {Curvature} {Tensors} by {Means} of {Young} {Symmetrizers}},
     journal = {S\'eminaire lotharingien de combinatoire},
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     year = {2002-2003},
     url = {http://geodesic.mathdoc.fr/item/SLC_2002-2003_48_a3/}
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Bernd Fiedler. Determination of the Structure of Algebraic Curvature Tensors by Means of Young Symmetrizers. Séminaire lotharingien de combinatoire, Tome 48 (2002-2003). http://geodesic.mathdoc.fr/item/SLC_2002-2003_48_a3/