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The subspaces and orthonormal bases of symmetry classes of tensors. (English) Zbl 0751.15013
Some methods for constructing orthonormal bases of the symmetry classes of tensors are given and a set of theorems is proved showing how to construct an orthonormal basis of a given unitary, irreducible representation of \(G\), where \(G\) is the subgroup of the full symmetric group of tensors. Several examples for constructing orthonormal bases of symmetry classes of tensors are also worked out numerically.

15A72 Vector and tensor algebra, theory of invariants
Full Text: DOI
[1] DOI: 10.1080/03081087308817022 · Zbl 0284.15025 · doi:10.1080/03081087308817022
[2] DOI: 10.1016/S0024-3795(73)80004-7 · Zbl 0283.15004 · doi:10.1016/S0024-3795(73)80004-7
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[4] DOI: 10.1080/03081087808817235 · Zbl 0396.15015 · doi:10.1080/03081087808817235
[5] DOI: 10.1080/03081088608817710 · Zbl 0591.15020 · doi:10.1080/03081088608817710
[6] DOI: 10.1080/03081088708817782 · Zbl 0621.15022 · doi:10.1080/03081088708817782
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