Results for Point Group Td



Symmetric powers of degenerate representation T1
Vibrational overtones


Characters of symmetric powers
Power
To
E 8C3 3C2 6S4 d
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 1 0 T1
2 1 0 1 0 1 A1⊕E⊕T2
3 0 1 0 2 1 A2⊕2T1⊕T2
4 2 0 2 1 2 2A1⊕2E⊕T1⊕2T2
5 0 1 1 4 2 A2⊕E⊕4T1⊕2T2
6 3 1 3 2 4 3A1⊕A2⊕3E⊕2T1⊕4T2
7 0 2 2 6 4 2A2⊕2E⊕6T1⊕4T2
8 4 1 5 4 6 4A1⊕A2⊕5E⊕4T1⊕6T2
9 1 3 3 9 6 A1⊕3A2⊕3E⊕9T1⊕6T2
10 5 2 7 6 9 5A1⊕2A2⊕7E⊕6T1⊕9T2
11 1 4 5 12 9 A1⊕4A2⊕5E⊕12T1⊕9T2
12 7 3 9 9 12 7A1⊕3A2⊕9E⊕9T1⊕12T2
13 2 5 7 16 12 2A1⊕5A2⊕7E⊕16T1⊕12T2
14 8 4 12 12 16 8A1⊕4A2⊕12E⊕12T1⊕16T2
15 3 7 9 20 16 3A1⊕7A2⊕9E⊕20T1⊕16T2
16 10 5 15 16 20 10A1⊕5A2⊕15E⊕16T1⊕20T2
17 4 8 12 25 20 4A1⊕8A2⊕12E⊕25T1⊕20T2
18 12 7 18 20 25 12A1⊕7A2⊕18E⊕20T1⊕25T2
19 5 10 15 30 25 5A1⊕10A2⊕15E⊕30T1⊕25T2
20 14 8 22 25 30 14A1⊕8A2⊕22E⊕25T1⊕30T2



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