Vector multiplication, vibration-rotation

This very usefiil result is the basis of the projection operator method. The projection is the use of the operations from the group to give the effect for a particular generating basis vector, e.g. a C2 rotation transforms b into f>2- The character multiplications give the correct relationship between the original and projected vector for the particular irreducible representation. In a B2 vibration (Figure 6.18c), the vector actually present at H2 is in the opposite direction to the C2 projection of b, and the multiplication by the appropriate... 

---