Results for Point Group D9h



Symmetric powers of degenerate representation E'3
Vibrational overtones


Characters of symmetric powers
Power
To
E 2C9 2(C9)2 2C3 2(C9)4 9C'2 σh 2S9 2(S9)7 2S3 2(S9)5 v
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
A'1 A'2 E'1 E'2 E'3 E'4 A''1 A''2 E''1 E''2 E''3 E''4
1 0 0 0 0 1 0 0 0 0 0 0 0 E'3
2 1 0 0 0 1 0 0 0 0 0 0 0 A'1⊕E'3
3 1 1 0 0 1 0 0 0 0 0 0 0 A'1⊕A'2⊕E'3
4 1 0 0 0 2 0 0 0 0 0 0 0 A'1⊕2E'3
5 1 1 0 0 2 0 0 0 0 0 0 0 A'1⊕A'2⊕2E'3
6 2 1 0 0 2 0 0 0 0 0 0 0 2A'1⊕A'2⊕2E'3
7 1 1 0 0 3 0 0 0 0 0 0 0 A'1⊕A'2⊕3E'3
8 2 1 0 0 3 0 0 0 0 0 0 0 2A'1⊕A'2⊕3E'3
9 2 2 0 0 3 0 0 0 0 0 0 0 2A'1⊕2A'2⊕3E'3
10 2 1 0 0 4 0 0 0 0 0 0 0 2A'1⊕A'2⊕4E'3
11 2 2 0 0 4 0 0 0 0 0 0 0 2A'1⊕2A'2⊕4E'3
12 3 2 0 0 4 0 0 0 0 0 0 0 3A'1⊕2A'2⊕4E'3
13 2 2 0 0 5 0 0 0 0 0 0 0 2A'1⊕2A'2⊕5E'3
14 3 2 0 0 5 0 0 0 0 0 0 0 3A'1⊕2A'2⊕5E'3
15 3 3 0 0 5 0 0 0 0 0 0 0 3A'1⊕3A'2⊕5E'3
16 3 2 0 0 6 0 0 0 0 0 0 0 3A'1⊕2A'2⊕6E'3
17 3 3 0 0 6 0 0 0 0 0 0 0 3A'1⊕3A'2⊕6E'3
18 4 3 0 0 6 0 0 0 0 0 0 0 4A'1⊕3A'2⊕6E'3
19 3 3 0 0 7 0 0 0 0 0 0 0 3A'1⊕3A'2⊕7E'3
20 4 3 0 0 7 0 0 0 0 0 0 0 4A'1⊕3A'2⊕7E'3



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