Spinor representations of space groups

Example 16.8-1 Determine the spinor representations for space group 219 (F43c or T ) at the symmetry points X and W. 

The character table ofD2d shows the five vector representations A, A2, B2, E which we 

These characters are real and therefore no additional degeneracies are to be expected in crystals exhibiting time-reversal symmetry. 

The IRs and their characters are given in Table 16.21. The space-group representations are obtained by multiplying these 1-D IRs in Table 16.21 by the MRs of T(k). 

Exercise 16.8-3 Write down the quaternion parameters for R c S4 and hence verify the matrices in Table 16.21. 

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