Reduction formula for point group C2v
Characters of input representation
E |
C2 (z) |
v(xz) |
v(yz) |
6 |
0 |
4 |
2 |
Decomposition into Irreducible representations
A1 |
A2 |
B1 |
B2 |
3 |
0 |
2 |
1 |
Symmetric Powers of Representation
Characters of symmetric powers
Tensor Order |
E |
C2 (z) |
v(xz) |
v(yz) |
1 |
6 |
0 |
4 |
2 |
2 |
21 |
3 |
11 |
5 |
3 |
56 |
0 |
24 |
8 |
4 |
126 |
6 |
46 |
14 |
5 |
252 |
0 |
80 |
20 |
6 |
462 |
10 |
130 |
30 |
Decomposition into Irreducible representations
Tensor Order |
A1 |
A2 |
B1 |
B2 |
1 |
3 |
0 |
2 |
1 |
2 |
10 |
2 |
6 |
3 |
3 |
22 |
6 |
18 |
10 |
4 |
48 |
18 |
38 |
22 |
5 |
88 |
38 |
78 |
48 |
6 |
158 |
78 |
138 |
88 |
Antisymmetric Powers of Representation
Characters of antisymmetric powers
Tensor Order |
E |
C2 (z) |
v(xz) |
v(yz) |
1 | 6 |
0 |
4 |
2 |
2 | 15 |
-3 |
5 |
-1 |
3 | 20 |
0 |
0 |
-4 |
4
| 15 |
3 |
-5 |
-1 |
5
| 6 |
0 |
-4 |
2 |
6
*
| 1 |
-1 |
-1 |
1 |
* Tensor rank equal tensor order
Decomposition into Irreducible representations
Tensor Order |
A1 |
A2 |
B1 |
B2 |
1
| 3 |
0 |
2 |
1 |
2
| 4 |
2 |
6 |
3 |
3
| 4 |
6 |
6 |
4 |
4
| 3 |
6 |
2 |
4 |
5
| 1 |
2 |
0 |
3 |
6
*
| 0 |
0 |
0 |
1 |
* Tensor rank equal tensor order
Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement