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 0 0 0 0 0 0 1 0 E''3
2 1 0 0 0 1 0 0 0 0 0 0 0 A'1⊕E'3
3 0 0 0 0 0 0 1 1 0 0 1 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 0 0 0 0 0 0 1 1 0 0 2 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 0 0 0 0 0 0 1 1 0 0 3 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 0 0 0 0 0 0 2 2 0 0 3 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 0 0 0 0 0 0 2 2 0 0 4 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 0 0 0 0 0 0 2 2 0 0 5 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 0 0 0 0 0 0 3 3 0 0 5 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 0 0 0 0 0 0 3 3 0 0 6 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 0 0 0 0 0 0 3 3 0 0 7 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