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 Constructor University Bremen
Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement