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2002-22

A Note on the Orthogonal Basis of a Certain Full Symmetry Class of Tensors

by Bessenrodt, C., Pournaki, M. R., Reifegerste, A..


Series: 2002-22, Preprints

MSC:
20C30 Representations of finite symmetric groups
15A69 Multilinear algebra, tensor products

Abstract:
It is shown that the full symmetry class of tensors associated with the
irreducible character $[2, 1^{n-2}]$ of $S_n$ does not have an orthogonal
basis consisting of decomposable symmetrized tensors.

Keywords:
(Full) symmetry class of tensors, orthogonal basis, decomposable symmetrized tensor, irreducible characters of the symmetric group