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Representation Products:
| ⊗ |
A1 |
A2 |
B1 |
B2 |
E1 |
E2 |
E3 |
| A1 |
A1 |
A2 |
B1 |
B2 |
E1 |
E2 |
E3 |
| A2 |
A2 |
A1 |
B2 |
B1 |
E1 |
E2 |
E3 |
| B1 |
B1 |
B2 |
A1 |
A2 |
E3 |
E2 |
E1 |
| B2 |
B2 |
B1 |
A2 |
A1 |
E3 |
E2 |
E1 |
| E1 |
E1 |
E1 |
E3 |
E3 |
A1+A2+E2 |
E1+E3 |
B1+B2+E2 |
| E2 |
E2 |
E2 |
E2 |
E2 |
E1+E3 |
A1+A2+B1+B2 |
E1+E3 |
| E3 |
E3 |
E3 |
E1 |
E1 |
B1+B2+E2 |
E1+E3 |
A1+A2+E2 |
Transition Products:
For the D4d point group, the irreducible representation of the dipole operator is (B2+E1). Transitions that are dipole forbidden are indicated by parentheses.
| ⊗(B2+E1)⊗ |
A1 |
A2 |
B1 |
B2 |
E1 |
E2 |
E3 |
| A1 |
(B2+E1) |
(B1+E1) |
(A2+E3) |
A1+E3 |
A1+A2+E2+E3 |
(E1+E2+E3) |
(B1+B2+E1+E2) |
| A2 |
(B1+E1) |
(B2+E1) |
A1+E3 |
(A2+E3) |
A1+A2+E2+E3 |
(E1+E2+E3) |
(B1+B2+E1+E2) |
| B1 |
(A2+E3) |
A1+E3 |
(B2+E1) |
(B1+E1) |
(B1+B2+E1+E2) |
(E1+E2+E3) |
A1+A2+E2+E3 |
| B2 |
A1+E3 |
(A2+E3) |
(B1+E1) |
(B2+E1) |
(B1+B2+E1+E2) |
(E1+E2+E3) |
A1+A2+E2+E3 |
| E1 |
A1+A2+E2+E3 |
A1+A2+E2+E3 |
(B1+B2+E1+E2) |
(B1+B2+E1+E2) |
(B1+B2+3E1+E2+E3) |
A1+A2+B1+B2+E1+2E2+E3 |
A1+A2+E1+E2+3E3 |
| E2 |
(E1+E2+E3) |
(E1+E2+E3) |
(E1+E2+E3) |
(E1+E2+E3) |
A1+A2+B1+B2+E1+2E2+E3 |
A1+A2+B1+B2+2E1+2E3 |
A1+A2+B1+B2+E1+2E2+E3 |
| E3 |
(B1+B2+E1+E2) |
(B1+B2+E1+E2) |
A1+A2+E2+E3 |
A1+A2+E2+E3 |
A1+A2+E1+E2+3E3 |
A1+A2+B1+B2+E1+2E2+E3 |
(B1+B2+3E1+E2+E3) |
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