Working with characters and irreducible representations

This tutorial explains the basic functionality of GTPack for working with characters and irreducible representations.

GTInstallGroup[group]Installation of a point group
GTCharacterTable[group]Calculation of the character table
We choose the point group C3v which is installed using GTInstallGroup.
The character system of a point group is installed with GTCharacterTable. The option GOIrepNotation controls the names of the irreducible representations. The default is the Bethe notation, naming irreducible representations with a dummy index.
Alternatives are the Mulliken notation (The Journal of Chemical Physics, AIP, 23, 1997-2011, (1953)) as well as the Bouckaert notation (L. Bouckaert, R. Smoluchowski and E. Wigner, Phys. Rev., APS, 50, 58-67 (1936)) .
GTAngularMomentumChars[classes,l]Calculation of the characters of the angular momentum representation.
GTIrep[characters,character table]Calculates, how often an irreducible representation occurs within a reducible representation.
GTGetIreps[group]Calculates the representation matrices and the character table.
To calculate the energy level splitting for atoms or molecules, the character of the (2l+1)-dimensional representation matrices of the angular momentum operator are calculated using GTAngularMomentumChars.
To reduce a faithful representation and to calculate the number of times, an irreducible representation occurs within a reducible representation, GTIrep is used.
All representation matrices together with the character table are obtained using GTGetIreps.
GTDirectProductChars[characters1,characters2]Calculates the characters of a direct product representation from two given character systems.
For unitary representations Γ1 and Γ2 the characters of the direct product presentation Γ1⊗ are given by χ(T) = χ1(T)χ2(T). If two character systems are known, GTDirectProductRepresentation calculates the character system of the direct product representation.