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Manuscript Title: Numerical calculations of the irreducible representations of space groups.
Authors: N. Neto
Program title: SPACE GROUP REPRESENTATIONS
Catalogue identifier: ACUA_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 9(1975)231
Programming language: Fortran.
Computer: CII 10070.
Operating system: SIRIS 7.
RAM: 46K words
Word size: 32
Keywords: Solid state physics, Group theory, Space groups, Lattice dynamics, Irreducible Representations.
Classification: 7.8.

Nature of problem:
The program computes the irreducible representations of any space group of k, G(k), where k is a wave vector in the first Brillouin zone. For each irreducible representation of G(k) a set of matrices, one for each space group coset representative, is obtained. No particular choice of origin of the coordinate system in a space group G is required.

Solution method:
A definition of 1 up to 3 generators of the space group G is used to obtain the multiplication properties of all coset representatives in G. An induction method is applied to compute the irreducible represent- ations of G(k). Herring's criterion provides a check for the existence of extra degeneracy due to time-reversal symmetry.

Restrictions:
This program is dimensioned for any space group, symmorphic or non- symmorphic, and for any value k in the first Brillouin zone. No restriction is placed on the choice of the origin of the coordinate system in the space group. Complex algebra is used and matrix elements for the irreducible representations are obtained as complex numbers.

Unusual features:
The irreducible representations, and the corresponding character tables, are printed out in symbolic form and symbols for point group elements are identified by maximally four alphanumeric characters, closely related to the usual Schroenflies notation.

Running time:
0.68 min were necessary for computing the irreducible representations of the space group T6h (Pa 3) for 14 different high-symmetry wave vectors.