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YoungSymmetrize[expr, tab]
symmetrizes the tensorial expression expr with respect to the Young tableau tab.
  • The symmetrization is with unit normalization, thus e.g. YoungSymmetrize[ T[a,b], {{a,b}} ] gives 1/2 T[a,b] + 1/2 T[b,a].
  • The Young tableau has to be given as an array. For example, the array {{a, b}, {c, d}} represents the tableau . See also YoungTableauQ.
  • The entries of the tableau tab have to be the set of free indices of expr.
  • The following options can be given:
ManifestSymmetryAntisymmetricwith what manifest symmetry the result is symmetrized
  • Possible settings for ManifestSymmetry include:
Antisymmetricfirst symmetrize rows and then antisymmetrize columns
Symmetricfirst antisymmetrize columns and then symmetrize rows