Results for Point Group C20



Symmetric powers of degenerate representation E6
Vibrational overtones


Characters of symmetric powers
Power
To		 E C20 C10 (C20)3 C5 C4 (C10)3 (C20)7 (C5)2 (C20)9 C2 (C20)11 (C5)3 (C20)13 (C10)7 (C4)3 (C5)4 (C20)17 (C10)9 (C20)19
1 2 -0.618 -1.618 1.618 0.618 -2 0.618 1.618 -1.618 -0.618 2 -0.618 -1.618 1.618 0.618 -2 0.618 1.618 -1.618 -0.618
2 3 -0.618 1.618 1.618 -0.618 3 -0.618 1.618 1.618 -0.618 3 -0.618 1.618 1.618 -0.618 3 -0.618 1.618 1.618 -0.618
3 4 1.000 -1.000 1.000 -1.000 -4 -1.000 1.000 -1.000 1.000 4 1.000 -1.000 1.000 -1.000 -4 -1.000 1.000 -1.000 1.000
4 5 0.000 0.000 -0.000 -0.000 5 0.000 0.000 -0.000 -0.000 5 0.000 0.000 -0.000 -0.000 5 0.000 0.000 -0.000 -0.000
5 6 -1.000 1.000 -1.000 1.000 -6 1.000 -1.000 1.000 -1.000 6 -1.000 1.000 -1.000 1.000 -6 1.000 -1.000 1.000 -1.000
6 7 0.618 -1.618 -1.618 0.618 7 0.618 -1.618 -1.618 0.618 7 0.618 -1.618 -1.618 0.618 7 0.618 -1.618 -1.618 0.618
7 8 0.618 1.618 -1.618 -0.618 -8 -0.618 -1.618 1.618 0.618 8 0.618 1.618 -1.618 -0.618 -8 -0.618 -1.618 1.618 0.618
8 9 -1.000 -1.000 -1.000 -1.000 9 -1.000 -1.000 -1.000 -1.000 9 -1.000 -1.000 -1.000 -1.000 9 -1.000 -1.000 -1.000 -1.000
9 10 -0.000 0.000 0.000 -0.000 -10 0.000 -0.000 -0.000 0.000 10 -0.000 0.000 0.000 -0.000 -10 0.000 -0.000 -0.000 0.000
10 11 1.000 1.000 1.000 1.000 11 1.000 1.000 1.000 1.000 11 1.000 1.000 1.000 1.000 11 1.000 1.000 1.000 1.000
11 12 -0.618 -1.618 1.618 0.618 -12 0.618 1.618 -1.618 -0.618 12 -0.618 -1.618 1.618 0.618 -12 0.618 1.618 -1.618 -0.618
12 13 -0.618 1.618 1.618 -0.618 13 -0.618 1.618 1.618 -0.618 13 -0.618 1.618 1.618 -0.618 13 -0.618 1.618 1.618 -0.618
13 14 1.000 -1.000 1.000 -1.000 -14 -1.000 1.000 -1.000 1.000 14 1.000 -1.000 1.000 -1.000 -14 -1.000 1.000 -1.000 1.000
14 15 0.000 0.000 -0.000 -0.000 15 0.000 0.000 -0.000 -0.000 15 0.000 0.000 -0.000 -0.000 15 0.000 0.000 -0.000 -0.000
15 16 -1.000 1.000 -1.000 1.000 -16 1.000 -1.000 1.000 -1.000 16 -1.000 1.000 -1.000 1.000 -16 1.000 -1.000 1.000 -1.000
16 17 0.618 -1.618 -1.618 0.618 17 0.618 -1.618 -1.618 0.618 17 0.618 -1.618 -1.618 0.618 17 0.618 -1.618 -1.618 0.618
17 18 0.618 1.618 -1.618 -0.618 -18 -0.618 -1.618 1.618 0.618 18 0.618 1.618 -1.618 -0.618 -18 -0.618 -1.618 1.618 0.618
18 19 -1.000 -1.000 -1.000 -1.000 19 -1.000 -1.000 -1.000 -1.000 19 -1.000 -1.000 -1.000 -1.000 19 -1.000 -1.000 -1.000 -1.000
19 20 -0.000 0.000 0.000 -0.000 -20 0.000 -0.000 -0.000 0.000 20 -0.000 0.000 0.000 -0.000 -20 0.000 -0.000 -0.000 0.000
20 21 1.000 1.000 1.000 1.000 21 1.000 1.000 1.000 1.000 21 1.000 1.000 1.000 1.000 21 1.000 1.000 1.000 1.000


Decomposition to irreducible representations
Power
To		 A B E1* E2* E3* E4* E5* E6* E7* E8* E9*
1 0 0 0 0 0 0 0 1 0 0 0 E6
2 1 0 0 0 0 0 0 0 0 1 0 A⊕E8
3 0 0 0 1 0 0 0 1 0 0 0 E2⊕E6
4 1 0 0 0 0 1 0 0 0 1 0 A⊕E4⊕E8
5 0 2 0 1 0 0 0 1 0 0 0 2B⊕E2⊕E6
6 1 0 0 0 0 2 0 0 0 1 0 A⊕2E4⊕E8
7 0 2 0 2 0 0 0 1 0 0 0 2B⊕2E2⊕E6
8 1 0 0 0 0 2 0 0 0 2 0 A⊕2E4⊕2E8
9 0 2 0 2 0 0 0 2 0 0 0 2B⊕2E2⊕2E6
10 3 0 0 0 0 2 0 0 0 2 0 3A⊕2E4⊕2E8
11 0 2 0 2 0 0 0 3 0 0 0 2B⊕2E2⊕3E6
12 3 0 0 0 0 2 0 0 0 3 0 3A⊕2E4⊕3E8
13 0 2 0 3 0 0 0 3 0 0 0 2B⊕3E2⊕3E6
14 3 0 0 0 0 3 0 0 0 3 0 3A⊕3E4⊕3E8
15 0 4 0 3 0 0 0 3 0 0 0 4B⊕3E2⊕3E6
16 3 0 0 0 0 4 0 0 0 3 0 3A⊕4E4⊕3E8
17 0 4 0 4 0 0 0 3 0 0 0 4B⊕4E2⊕3E6
18 3 0 0 0 0 4 0 0 0 4 0 3A⊕4E4⊕4E8
19 0 4 0 4 0 0 0 4 0 0 0 4B⊕4E2⊕4E6
20 5 0 0 0 0 4 0 0 0 4 0 5A⊕4E4⊕4E8


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