GroupTheory`
GroupTheory`

GTSymmetrizedProductChars

GTSymmetrizedProductChars[character table,number Irep,n,sign]

gives the characters of the symmetrized [T]^(n ) or antisymmetrized {T}^n n-th power of the irreducible representation of a group , represented by its character table.

Details and Options

  • The n-th power of an inrreducible representation of a group will be considered. The character of the symmetrized product and of the antisymmetrized product can be calculated directly from the character system of . Such product representations are used in group theoretical considerations to Landau’s theory of phase transitions.
  • The following options can be given:
  • GOVerbose TrueControls the output of additional information
  • See: W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica.
  • G. J. Ljubarski, Anwendungen der Gruppentheorie in der Physik. VEB Deutscher Verlag der Wissenschaften, Berlin 1962.
  • Yu. A. Izyumov and V. N. Syromyatnikov, Phase Transitions and Crystal Symmetry. Kluwer Academic Publishers, Dordrecht 1990.

Examples

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Basic Examples  (1)

First load the package:

Install a group and calculate the character table.

Calculate the symmetric and antisymmetric 2nd power of the two-dimensional representation of .

Options  (1)

GOVerbose  (1)

The output of the table can be suppressed. Here all chacters of the 5th symmetric power of C_(4v) are calculated.