Herring method for non-symmorphic space groups

In Sections 16.4-16.6 the problem of finding the representations of a space group G at any particular k point was solved by reducing the size of the group of the wave vector 

The law of binary composition in (k) is the Herring multiplication rule, which is the Seitz rule for the multiplication of space-group elements supplemented by the additional condition that ( t) is to be replaced by ( 0) whenever exp(—ik t) = + 1. 

The steps involved in Herring s method for a non-symmorphic space group will now be summarized as was done for the PR method in Section 16.6. 

On using eqs. (16.6.9) and (16.6.10) the matrices of the required representations found in (viii) give the elements Tk of the supermatrix as in step (vi) of Section 16.6, and these matrices, when multiplied by Tk(C t), are the space-group representations. 

Comment The required representations are also referred to in the literature as permitted or allowed representations. 

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