Algebraic Method to obtain Irreducible Representations of Space Groups with an Application to White Tin

Algebraic method to construct irreducible representations of space groups is presented by making an example of white tin having screw axes and glide planes in the symmetry operations. In present method it is enough to treat explicitly at most only symmetry elements equal in number to the operations of the point group to which concerned lattice belongs, regardless of the cases with or without spin and also of interior points or the points of the Brillouin zone boundary. This becomes very simplification compared to usual group-theoretical method.