Results for Point Group D20d



Symmetric powers of degenerate representation E4
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 1.618 0.618 -0.618 -1.618 -2.000 -1.618 -0.618 0.618 1.618 2 1.618 0.618 -0.618 -1.618 -2.000 -1.618 -0.618 0.618 1.618 2 0 0
2 3 1.618 -0.618 -0.618 1.618 3.000 1.618 -0.618 -0.618 1.618 3 1.618 -0.618 -0.618 1.618 3.000 1.618 -0.618 -0.618 1.618 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 -1.618 0.618 0.618 -1.618 7.000 -1.618 0.618 0.618 -1.618 7 -1.618 0.618 0.618 -1.618 7.000 -1.618 0.618 0.618 -1.618 7 1 1
7 8 -1.618 -0.618 0.618 1.618 -8.000 1.618 0.618 -0.618 -1.618 8 -1.618 -0.618 0.618 1.618 -8.000 1.618 0.618 -0.618 -1.618 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 1.618 0.618 -0.618 -1.618 -12.000 -1.618 -0.618 0.618 1.618 12 1.618 0.618 -0.618 -1.618 -12.000 -1.618 -0.618 0.618 1.618 12 0 0
12 13 1.618 -0.618 -0.618 1.618 13.000 1.618 -0.618 -0.618 1.618 13 1.618 -0.618 -0.618 1.618 13.000 1.618 -0.618 -0.618 1.618 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 -1.618 0.618 0.618 -1.618 17.000 -1.618 0.618 0.618 -1.618 17 -1.618 0.618 0.618 -1.618 17.000 -1.618 0.618 0.618 -1.618 17 1 1
17 18 -1.618 -0.618 0.618 1.618 -18.000 1.618 0.618 -0.618 -1.618 18 -1.618 -0.618 0.618 1.618 -18.000 1.618 0.618 -0.618 -1.618 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 E4
2 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 A1⊕E8
3 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 E4⊕E12
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 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 B1⊕B2⊕E4⊕E12
6 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 2 0 0 0 A1⊕E8⊕2E16
7 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 B1⊕B2⊕E4⊕2E12
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 0 0 1 1 0 0 0 2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 B1⊕B2⊕2E4⊕2E12
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 0 0 1 1 0 0 0 3 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 B1⊕B2⊕3E4⊕2E12
12 2 1 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 2 0 0 0 2A1⊕A2⊕3E8⊕2E16
13 0 0 1 1 0 0 0 3 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 B1⊕B2⊕3E4⊕3E12
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 0 0 2 2 0 0 0 3 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 2B1⊕2B2⊕3E4⊕3E12
16 2 1 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 4 0 0 0 2A1⊕A2⊕3E8⊕4E16
17 0 0 2 2 0 0 0 3 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 2B1⊕2B2⊕3E4⊕4E12
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 0 0 2 2 0 0 0 4 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 2B1⊕2B2⊕4E4⊕4E12
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 November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement