Irreducible representations of space groups

A method is presented for obtaining the matrices for the single-valued irreducible representations of any space group. Although the method is designed for computer handling of all algebraic steps, it may be easily applied for hand calculations. The procedure is based on the reduction of representations of a space group of the wave vector k induced by the irreducible representations of its invariant subgroup of index 2 or 3. For almost all space groups only the irreducible representations of a cyclic point group, i.e. the nth roots of unity for a generator of the group, are needed. Cubic space groups, for k values corresponding to high-symmetry points on the Brillouin zone boundary, are discussed in detail.