Representation Theory

Characters

GTCharacterTable — gives the character table of a group.

GTExtraRepresentations — extracts the extra representations from the character table.

GTReorderCharacterTable — gives the reordered character table of a group.

GTReality — estimates if a representation is real or complex or other.

GTSpinCharacters — gives the character of the spinor representation for each class.

GTSOCSplitting — calculates the splitting of states due to spin-orbit coupling.

Projection operators

GTCharProjectionOperator — applies the character projection operator to a given function.

GTProjectionOperator — applies the projection operator to a given function.

GTWignerProjectionOperator — applies the projection operator on spherical harmonics.

Auxiliary representations

GTAngularMomentumChars — calculates the character system using representation matrices.

GTAngularMomentumRep — gives a matrix representation using the WignerD-function.

GTRegularRepresentation — gives the regular representation of a group.

Irreducible representations

GTClebschGordanSum — calculates a matrix representation using the direct sum of two representations.

GTGetIreps — calculates the character table and irreducible representation matrices of a group

GTGetIrep — calculates the representation matrices of an irreducible representation.

GTIrep — gives the number of times an irreducible representation appears in a faithful representation.

GTIrepDimension — gives the dimension of an irreducible representation

GTIrepMatrixView — gives a neat print of the matrices of the irreducible representation.

GTNumberOfIreps — gives the number of non-equivalent irreducible representations.

Direct product representations

GTClebschGordanCoefficients — gives an array containing Clebsch-Gordan-Coefficients for the calculation of basis functions within a direct product representation.

GTClebschGordanTable — represents a list of Clebsch-Gordan-Coefficients

GTDirectProductChars — gives the character system of a direct product representation from the character systems of two representations.

GTDirectProductRep — calculates the direct product representation of two representations.

GTSymmetrizedProductChars — gives character of symmetrized or antisymmetrized n-th power of an irreducible representation