Results for Point Group D9d



Symmetric powers of degenerate representation E3g
Vibrational overtones


Characters of symmetric powers
Power
To
E 2C9 2(C9)2 2C3 2(C9)4 9C'2 i 2(S18)7 2(S18)5 2S6 2S18 d
1 2 -1.000 -1.000 2 -1.000 0 2 -1.000 -1.000 2 -1.000 0
2 3 0.000 0.000 3 0.000 1 3 0.000 0.000 3 0.000 1
3 4 1.000 1.000 4 1.000 0 4 1.000 1.000 4 1.000 0
4 5 -1.000 -1.000 5 -1.000 1 5 -1.000 -1.000 5 -1.000 1
5 6 0.000 0.000 6 0.000 0 6 0.000 0.000 6 0.000 0
6 7 1.000 1.000 7 1.000 1 7 1.000 1.000 7 1.000 1
7 8 -1.000 -1.000 8 -1.000 0 8 -1.000 -1.000 8 -1.000 0
8 9 0.000 0.000 9 0.000 1 9 0.000 0.000 9 0.000 1
9 10 1.000 1.000 10 1.000 0 10 1.000 1.000 10 1.000 0
10 11 -1.000 -1.000 11 -1.000 1 11 -1.000 -1.000 11 -1.000 1
11 12 0.000 0.000 12 0.000 0 12 0.000 0.000 12 0.000 0
12 13 1.000 1.000 13 1.000 1 13 1.000 1.000 13 1.000 1
13 14 -1.000 -1.000 14 -1.000 0 14 -1.000 -1.000 14 -1.000 0
14 15 0.000 0.000 15 0.000 1 15 0.000 0.000 15 0.000 1
15 16 1.000 1.000 16 1.000 0 16 1.000 1.000 16 1.000 0
16 17 -1.000 -1.000 17 -1.000 1 17 -1.000 -1.000 17 -1.000 1
17 18 0.000 0.000 18 0.000 0 18 0.000 0.000 18 0.000 0
18 19 1.000 1.000 19 1.000 1 19 1.000 1.000 19 1.000 1
19 20 -1.000 -1.000 20 -1.000 0 20 -1.000 -1.000 20 -1.000 0
20 21 0.000 0.000 21 0.000 1 21 0.000 0.000 21 0.000 1


Decomposition to irreducible representations
Power
To
A1g A2g E1g E2g E3g E4g A1u A2u E1u E2u E3u E4u
1 0 0 0 0 1 0 0 0 0 0 0 0 E3g
2 1 0 0 0 1 0 0 0 0 0 0 0 A1g⊕E3g
3 1 1 0 0 1 0 0 0 0 0 0 0 A1g⊕A2g⊕E3g
4 1 0 0 0 2 0 0 0 0 0 0 0 A1g⊕2E3g
5 1 1 0 0 2 0 0 0 0 0 0 0 A1g⊕A2g⊕2E3g
6 2 1 0 0 2 0 0 0 0 0 0 0 2A1g⊕A2g⊕2E3g
7 1 1 0 0 3 0 0 0 0 0 0 0 A1g⊕A2g⊕3E3g
8 2 1 0 0 3 0 0 0 0 0 0 0 2A1g⊕A2g⊕3E3g
9 2 2 0 0 3 0 0 0 0 0 0 0 2A1g⊕2A2g⊕3E3g
10 2 1 0 0 4 0 0 0 0 0 0 0 2A1g⊕A2g⊕4E3g
11 2 2 0 0 4 0 0 0 0 0 0 0 2A1g⊕2A2g⊕4E3g
12 3 2 0 0 4 0 0 0 0 0 0 0 3A1g⊕2A2g⊕4E3g
13 2 2 0 0 5 0 0 0 0 0 0 0 2A1g⊕2A2g⊕5E3g
14 3 2 0 0 5 0 0 0 0 0 0 0 3A1g⊕2A2g⊕5E3g
15 3 3 0 0 5 0 0 0 0 0 0 0 3A1g⊕3A2g⊕5E3g
16 3 2 0 0 6 0 0 0 0 0 0 0 3A1g⊕2A2g⊕6E3g
17 3 3 0 0 6 0 0 0 0 0 0 0 3A1g⊕3A2g⊕6E3g
18 4 3 0 0 6 0 0 0 0 0 0 0 4A1g⊕3A2g⊕6E3g
19 3 3 0 0 7 0 0 0 0 0 0 0 3A1g⊕3A2g⊕7E3g
20 4 3 0 0 7 0 0 0 0 0 0 0 4A1g⊕3A2g⊕7E3g



Last update January, 3rd 2020 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement