## Reduction formula for point group D4h

Characters of input representation
E 2C4 (z) C2 2C'2 2C''2 i 2S4 h 2v 2d
2 -2 2 0 0 0 0 0 2 -2

Decomposition into Irreducible representations
A1g A2g B1g B2g Eg A1u A2u B1u B2u Eu
0 0 1 0 0 0 0 0 1 0

### Symmetric Powers of Representation

Characters of symmetric powers
Tensor
Order
E 2C4 (z) C2 2C'2 2C''2 i 2S4 h 2v 2d
1 2 -2 2 0 0 0 0 0 2 -2
2 3 3 3 1 1 1 1 1 3 3
3 4 -4 4 0 0 0 0 0 4 -4
4 5 5 5 1 1 1 1 1 5 5
5 6 -6 6 0 0 0 0 0 6 -6
6 7 7 7 1 1 1 1 1 7 7

Decomposition into Irreducible representations
Tensor
Order
A1g A2g B1g B2g Eg A1u A2u B1u B2u Eu
1 0 0 1 0 0 0 0 0 1 0
2 2 0 0 0 0 0 1 0 0 0
3 0 0 2 0 0 0 0 0 2 0
4 3 0 0 0 0 0 2 0 0 0
5 0 0 3 0 0 0 0 0 3 0
6 4 0 0 0 0 0 3 0 0 0

### Antisymmetric Powers of Representation

Characters of antisymmetric powers
Tensor
Order
E 2C4 (z) C2 2C'2 2C''2 i 2S4 h 2v 2d
12 -2 2 0 0 0 0 0 2 -2
2* 1 1 1 -1 -1 -1 -1 -1 1 1
3** 0 0 0 0 0 0 0 0 0 0
4 ** 0 0 0 0 0 0 0 0 0 0
5 ** 0 0 0 0 0 0 0 0 0 0
6 ** 0 0 0 0 0 0 0 0 0 0
* Tensor rank equal tensor order
** Tensor rank less than tensor order

Decomposition into Irreducible representations
Tensor
Order
A1g A2g B1g B2g Eg A1u A2u B1u B2u Eu
1 0 0 1 0 0 0 0 0 1 0
2 * 0 0 0 0 0 0 1 0 0 0
3 ** 0 0 0 0 0 0 0 0 0 0
4 ** 0 0 0 0 0 0 0 0 0 0
5 ** 0 0 0 0 0 0 0 0 0 0
6 ** 0 0 0 0 0 0 0 0 0 0
* Tensor rank equal tensor order
** Tensor rank less than tensor order

Last update Mai, 23rd 2018 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement