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





Character tables for chemically important point groups Character table for point group D4h Jacobs University Bremen

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