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That this will work in this case, because there is the possibility that none of theĮlements (besides the identity) are diagonal in the reduced representation. See if the same transformation puts them into a reduced form. We will diagonalize one of the group elements, and then check the other elements to We can attempt to reduce this matrix by a similar process to the one used earlier. Table 15 and we will refer to this as the DY] representation. The other group elements are constructed in a similar manner. This matrix is a valid representation for the g3 element of D3. Generates the sequence ( h a ) from the sequence ( a h ). As always, zyxwvutsDyl is the trivial one-dimensional irreducible representation.Ī 3 X 3 matrix representation for this group can be constructed from the operator Therefore, it is an irreduciblerepresentation, which we will call DY]. AnĪttempt to diagonalize this representation in the same way we did for the previousĮxample fails. We showed a 2 zyxwvuX 2 matrix representation for this group in Table 15. Example zyxwvu15 As another example of representation reduction, consider the 0 3 group. Orthogonality relations of the irreduciblerepresentations, a topic we explore later in A more educational method is to derive it using the

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