Results for Point Group D20d



Symmetric powers of degenerate representation E8
Vibrational overtones


Characters of symmetric powers
Power
To
E 2S40 2C20 2(S40)3 2C10 2S8 2(C20)3 2(S40)7 2C5 2(S40)9 2C4 2(S40)11 2(C10)3 2(S40)13 2(C20)7 2(S8)3 2(C5)2 2(S40)17 2(C20)9 2(S40)19 C2 20C'2 20σd
1 2 0.618 -1.618 -1.618 0.618 2.000 0.618 -1.618 -1.618 0.618 2 0.618 -1.618 -1.618 0.618 2.000 0.618 -1.618 -1.618 0.618 2 0 0
2 3 -0.618 1.618 1.618 -0.618 3.000 -0.618 1.618 1.618 -0.618 3 -0.618 1.618 1.618 -0.618 3.000 -0.618 1.618 1.618 -0.618 3 1 1
3 4 -1.000 -1.000 -1.000 -1.000 4.000 -1.000 -1.000 -1.000 -1.000 4 -1.000 -1.000 -1.000 -1.000 4.000 -1.000 -1.000 -1.000 -1.000 4 0 0
4 5 -0.000 -0.000 0.000 0.000 5.000 -0.000 -0.000 0.000 0.000 5 -0.000 0.000 -0.000 0.000 5.000 -0.000 -0.000 0.000 0.000 5 1 1
5 6 1.000 1.000 1.000 1.000 6.000 1.000 1.000 1.000 1.000 6 1.000 1.000 1.000 1.000 6.000 1.000 1.000 1.000 1.000 6 0 0
6 7 0.618 -1.618 -1.618 0.618 7.000 0.618 -1.618 -1.618 0.618 7 0.618 -1.618 -1.618 0.618 7.000 0.618 -1.618 -1.618 0.618 7 1 1
7 8 -0.618 1.618 1.618 -0.618 8.000 -0.618 1.618 1.618 -0.618 8 -0.618 1.618 1.618 -0.618 8.000 -0.618 1.618 1.618 -0.618 8 0 0
8 9 -1.000 -1.000 -1.000 -1.000 9.000 -1.000 -1.000 -1.000 -1.000 9 -1.000 -1.000 -1.000 -1.000 9.000 -1.000 -1.000 -1.000 -1.000 9 1 1
9 10 -0.000 -0.000 0.000 0.000 10.000 -0.000 -0.000 0.000 0.000 10 -0.000 0.000 0.000 0.000 10.000 -0.000 -0.000 0.000 0.000 10 0 0
10 11 1.000 1.000 1.000 1.000 11.000 1.000 1.000 1.000 1.000 11 1.000 1.000 1.000 1.000 11.000 1.000 1.000 1.000 1.000 11 1 1
11 12 0.618 -1.618 -1.618 0.618 12.000 0.618 -1.618 -1.618 0.618 12 0.618 -1.618 -1.618 0.618 12.000 0.618 -1.618 -1.618 0.618 12 0 0
12 13 -0.618 1.618 1.618 -0.618 13.000 -0.618 1.618 1.618 -0.618 13 -0.618 1.618 1.618 -0.618 13.000 -0.618 1.618 1.618 -0.618 13 1 1
13 14 -1.000 -1.000 -1.000 -1.000 14.000 -1.000 -1.000 -1.000 -1.000 14 -1.000 -1.000 -1.000 -1.000 14.000 -1.000 -1.000 -1.000 -1.000 14 0 0
14 15 -0.000 -0.000 0.000 0.000 15.000 -0.000 -0.000 0.000 0.000 15 -0.000 0.000 0.000 0.000 15.000 -0.000 -0.000 0.000 0.000 15 1 1
15 16 1.000 1.000 1.000 1.000 16.000 1.000 1.000 1.000 1.000 16 1.000 1.000 1.000 1.000 16.000 1.000 1.000 1.000 1.000 16 0 0
16 17 0.618 -1.618 -1.618 0.618 17.000 0.618 -1.618 -1.618 0.618 17 0.618 -1.618 -1.618 0.618 17.000 0.618 -1.618 -1.618 0.618 17 1 1
17 18 -0.618 1.618 1.618 -0.618 18.000 -0.618 1.618 1.618 -0.618 18 -0.618 1.618 1.618 -0.618 18.000 -0.618 1.618 1.618 -0.618 18 0 0
18 19 -1.000 -1.000 -1.000 -1.000 19.000 -1.000 -1.000 -1.000 -1.000 19 -1.000 -1.000 -1.000 -1.000 19.000 -1.000 -1.000 -1.000 -1.000 19 1 1
19 20 -0.000 -0.000 0.000 0.000 20.000 -0.000 -0.000 0.000 0.000 20 -0.000 0.000 0.000 0.000 20.000 -0.000 -0.000 0.000 0.000 20 0 0
20 21 1.000 1.000 1.000 1.000 21.000 1.000 1.000 1.000 1.000 21 1.000 1.000 1.000 1.000 21.000 1.000 1.000 1.000 1.000 21 1 1


Decomposition to irreducible representations
Power
To
A1 A2 B1 B2 E1 E2 E3 E4 E5 E6 E7 E8 E9 E10 E11 E12 E13 E14 E15 E16 E17 E18 E19
1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 E8
2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 A1⊕E16
3 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 E8⊕E16
4 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 A1⊕E8⊕E16
5 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 A1⊕A2⊕E8⊕E16
6 1 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 1 0 0 0 A1⊕2E8⊕E16
7 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 2 0 0 0 A1⊕A2⊕E8⊕2E16
8 1 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 A1⊕2E8⊕2E16
9 1 1 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 A1⊕A2⊕2E8⊕2E16
10 2 1 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 2A1⊕A2⊕2E8⊕2E16
11 1 1 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 2 0 0 0 A1⊕A2⊕3E8⊕2E16
12 2 1 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 3 0 0 0 2A1⊕A2⊕2E8⊕3E16
13 1 1 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 3 0 0 0 A1⊕A2⊕3E8⊕3E16
14 2 1 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 3 0 0 0 2A1⊕A2⊕3E8⊕3E16
15 2 2 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 3 0 0 0 2A1⊕2A2⊕3E8⊕3E16
16 2 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 3 0 0 0 2A1⊕A2⊕4E8⊕3E16
17 2 2 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 4 0 0 0 2A1⊕2A2⊕3E8⊕4E16
18 2 1 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 4 0 0 0 2A1⊕A2⊕4E8⊕4E16
19 2 2 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 4 0 0 0 2A1⊕2A2⊕4E8⊕4E16
20 3 2 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 4 0 0 0 3A1⊕2A2⊕4E8⊕4E16



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