Bilbao Crystallographic Server CoRepresentations

Notes on the notation of the co-representations in the Bilbao Crystallographic Server

The co-representations of a magnetic group are obtained from the irreducible representations of its unitary subgroup. For the notation of the co-representations of the little groups, the label of the co-representation is obtained from the label (or labels) of the corresponding irreducible representation(s). In those cases (in some type III groups) in which the label of the k-vector in the magnetic group is different from the label in the unitary subgroup, the notation includes as a prefix the label of the magnetic group.
In the tables of co-representations and in the following examples, the BNS setting is assumed.

Examples of the notation used for the co-representations of the little groups

Example 1: magnetic group Cmc211' (N. 36.173)

It is a magnetic group of type II (gray group), and its unitary subgroup is the space group Cmc21 (N. 36).

Example 2: magnetic group P4'21'm (N. 113.269)

It is a magnetic group of type III whose unitary subgroup is the space group Cmm2 (N. 33). The unitary operations are not in the standard setting of the space group. The transformation matrix to the standard setting is (1/2a-1/b,1/2a+1/2b,c;0,1/2,0)
Note that, in this example, if the prefix is omited, the resulting labels of the co-representations could be misleading.

Examples of the notation used for the full co-representations

Example 3: magnetic group I4' (N. 79.27)

It is a magnetic group of type III whose unitary subgroup is the space group C2 (N. 5). The unitary operations are not in the standard setting of the space group. The transformation matrix to the standard setting is (a-c,a,-b;0,0,0)