Some comments on the theory of space-group representations: I

It is suggested that the Brillouin zones conventionally used for triclinic, monoclinic and, perhaps, trigonal crystals are unnecessarily complicated and can usefully be simplified. Secondly, the use of induced representations of a space group G (the full-group method) and the use of small representations of the little groups, G k , of the wave vector k (the subgroup method) are compared. Thirdly, the authors discuss the various possible kinds of extra degeneracy which may be produced among the eigenfunctions of a particle or quasi- particle in a crystal as a result of the existence of time-reversal symmetry.