Results for Point Group O



Symmetric powers of degenerate representation T2
Vibrational overtones


Characters of symmetric powers
Power
To		 E 8C3 6C2 6C4 3C2
1 3 0 1 -1 -1
2 6 0 2 0 2
3 10 1 2 0 -2
4 15 0 3 1 3
5 21 0 3 -1 -3
6 28 1 4 0 4
7 36 0 4 0 -4
8 45 0 5 1 5
9 55 1 5 -1 -5
10 66 0 6 0 6
11 78 0 6 0 -6
12 91 1 7 1 7
13 105 0 7 -1 -7
14 120 0 8 0 8
15 136 1 8 0 -8
16 153 0 9 1 9
17 171 0 9 -1 -9
18 190 1 10 0 10
19 210 0 10 0 -10
20 231 0 11 1 11


Decomposition to irreducible representations
Power
To		 A1 A2 E T1 T2
1 0 0 0 0 1 T2
2 1 0 1 0 1 A1⊕E⊕T2
3 1 0 0 1 2 A1⊕T1⊕2T2
4 2 0 2 1 2 2A1⊕2E⊕T1⊕2T2
5 1 0 1 2 4 A1⊕E⊕2T1⊕4T2
6 3 1 3 2 4 3A1⊕A2⊕3E⊕2T1⊕4T2
7 2 0 2 4 6 2A1⊕2E⊕4T1⊕6T2
8 4 1 5 4 6 4A1⊕A2⊕5E⊕4T1⊕6T2
9 3 1 3 6 9 3A1⊕A2⊕3E⊕6T1⊕9T2
10 5 2 7 6 9 5A1⊕2A2⊕7E⊕6T1⊕9T2
11 4 1 5 9 12 4A1⊕A2⊕5E⊕9T1⊕12T2
12 7 3 9 9 12 7A1⊕3A2⊕9E⊕9T1⊕12T2
13 5 2 7 12 16 5A1⊕2A2⊕7E⊕12T1⊕16T2
14 8 4 12 12 16 8A1⊕4A2⊕12E⊕12T1⊕16T2
15 7 3 9 16 20 7A1⊕3A2⊕9E⊕16T1⊕20T2
16 10 5 15 16 20 10A1⊕5A2⊕15E⊕16T1⊕20T2
17 8 4 12 20 25 8A1⊕4A2⊕12E⊕20T1⊕25T2
18 12 7 18 20 25 12A1⊕7A2⊕18E⊕20T1⊕25T2
19 10 5 15 25 30 10A1⊕5A2⊕15E⊕25T1⊕30T2
20 14 8 22 25 30 14A1⊕8A2⊕22E⊕25T1⊕30T2


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