Symmetry plays an important role in nature as well as in mathematics. Many properties of matter can be expressed in terms of Cartesian tensors. The analysis of tensor symmetry can be simplified by decomposing tensors into irreducible parts that possess complete (permutation) symmetry in the sense of Young. This paper compiles well-known results and formulas from group theory to construct an algorithm for such analytical decomposition and provides its explicit realization for Cartesian tensors of small rank (from 2 to 4). The complete results are presented in tabular form.
Citation: Pasynok Sergey. On the complete (permutation) symmetry of Cartesian tensors according to Young in a space of given finite arbitrary dimensions[J]. Metascience in Aerospace, 2026, 3(1): 28-53. doi: 10.3934/mina.2026003
Symmetry plays an important role in nature as well as in mathematics. Many properties of matter can be expressed in terms of Cartesian tensors. The analysis of tensor symmetry can be simplified by decomposing tensors into irreducible parts that possess complete (permutation) symmetry in the sense of Young. This paper compiles well-known results and formulas from group theory to construct an algorithm for such analytical decomposition and provides its explicit realization for Cartesian tensors of small rank (from 2 to 4). The complete results are presented in tabular form.
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Pasynok Sergey. On the complete (permutation) symmetry of Cartesian tensors according to Young in a space of given finite arbitrary dimensions[J]. Metascience in Aerospace, 2026, 3(1): 28-53. doi: 10.3934/mina.2026003
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