Co-representations of magnetic point groups

Consider the group G = H, AH that contains unitary H and antiunitary AH operators. H is necessarily an invariant subgroup of G of index 2 and AH is a coset of H with coset representative A (which may be any one of the antiunitary operators of G) so that 

For example, A might be the time-reversal operator 0 (Section 13.4) 

Equations (7) and (10) confirm that 6. i forms a 2/-dimensional basis for G. The representation T based on (i] i ) has matrix representatives (MRs) 

Therefore E is equivalent to E (E EO if there is a unitary matrix U such that  

Suppose next that T a F then there exists a unitary matrix Z such that  

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Example 14.2-2 Find the co-representations of the magnetic point group Amm or C4v(C2v). Take Q = rr.A, with a the unit vector along [110]. 

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