Input Information

For its calculations, REPRES needs a file containing the generators for the space group of interest. There are two ways to provide these generators:

1. If you specify the group G by its sequential number, as listed in International Tables for Crystallography, vol.A . Space group symmetry (1995, 3rd ed. Dordrecht:Kluwer Academic Publishers), then the program uses the non-translational generators as listed in Tables (with origin choice 1, unique axis b, where applicable).
2. If your group is in a setting different from the default settings, you can give the transformation matrices to the corresponding default setting by clicking over "Nonstandard settings". The elements of the transformation matrix can be given either as decimals or fractions.

2. k-vector data

There are three different options of specifying the k-vector coefficients accepted by REPRES:

1. by referring the coefficients referred to the primitive bases of reciprocal space, as found in Cracknell, Davies, Miller and Love. Kronecker Product Tables (1979);
2. by the so-called conventional k-vector coefficients.  In this case the conventional coefficients  refer to the basis a*,b*,c* of the reciprocal lattice L* which is dual to the basis of a,b,c of G;
3. There is also a possibility to specify the k-vector by its  adjusted coefficients. Given a space group G, the symmorphic space group G_s which is isomorphic to the reciprocal space group can be determined using the following Table (Wintgen, 1942). From the Wyckoff positions of G_s one obtains a complete list of the adjusted coefficients of the special k-vectors.

Output data

Information on the space group G

• nontranslational generators of G given as a matrix-column pair, i.e. in 3x4 matrix form
• list of translational coset representatives of G given in 3x4 matrix form

k-vector data

• k-vector  coordinates in conventional basis
• star of the k-vector

Information on the little group L of the specified k-vector

• a set of coset representatives of G with respect to L
• a set of non-translational generators of L given as 3x4 matrix
• a set of translational coset representatives of L given as 3x4 matrix
• little-group irreducible representations presented in a matrix form for the elements of L in consecutive order. With the exception of 0, 1,-1, i and -i the complex matrix elements are listed by their phase angles in  [º] and by their moduli.

The program gives the full group irreducible representations of the non-translational generators of the space group in block-matrix form: for a given representation and  a generator, the program prints out the induction matrix  whose non-zero entries specified by its row and column indices, indicate a matrix block corresponding to a little-group matrix.