YoungProject[expr, tab]
projects the tensorial expression expr onto the Young tableau tab.
  • The difference between projecting with YoungProject and symmetrizing with YoungSymmetrize is that the projection has a different overall factor, such that repeatedly projecting does not change the result.
  • 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