Full representations of the double space groups based on the simple cubic lattice

Abstract

The generating matrices of the induced (full) representations for the space groups Pm3m(=O 1 h), Pn3n(=O 2 h), Pm3n(=O 3 h) and Pn3m(=O 4 h) have been calculated. We have considered the representations corresponding to four high-symmetry points Γ, R, X and M in the Brillouin zone. We give explicitly the generators and generating relations for the full irreducible representations induced from the small irreducible representations of Miller and Love (M-L). Using these generators and generating relations and the program written in ALGOL, for the computer ODRA 1204 we have calculated the matrices of the full irreducible representations of the full space groups G k Γ , G k R , G ⋇ k M and G ⋇ k X .