On the classification and enumeration of the irreducible co-representations of magnetic space groups

A generalization of Wintgen's method for classifying space-group representations is made to enable the infinite set of co-representations of magnetic space groups to be classified and enumerated. Using this method, all special points, lines and planes in the Brillouin zone model for magnetic crystals are identified. Arithmetic crystal-classes of magnetic space groups are introduced, fully listed and used to classify magnetic space groups and their co-representations, A version of Burnside's theorem adapted to co-representations is constructed and used to solve completely the enumeration problem of co-representations of magnetic space groups.