Results for Point Group S20



Symmetric powers of degenerate representation E8
Vibrational overtones


Characters of symmetric powers
Power
To		 E S20 C10 (S20)3 C5 S4 (C10)3 (S20)7 (C5)2 (S20)9 C2 (S20)11 (C5)3 (S20)13 (C10)7 (S4)3 (C5)4 (S20)17 (C10)9 (S20)19
1 2 -1.618 0.618 0.618 -1.618 2 -1.618 0.618 0.618 -1.618 2 -1.618 0.618 0.618 -1.618 2 -1.618 0.618 0.618 -1.618
2 3 1.618 -0.618 -0.618 1.618 3 1.618 -0.618 -0.618 1.618 3 1.618 -0.618 -0.618 1.618 3 1.618 -0.618 -0.618 1.618
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 -1.618 0.618 0.618 -1.618 7 -1.618 0.618 0.618 -1.618 7 -1.618 0.618 0.618 -1.618 7 -1.618 0.618 0.618 -1.618
7 8 1.618 -0.618 -0.618 1.618 8 1.618 -0.618 -0.618 1.618 8 1.618 -0.618 -0.618 1.618 8 1.618 -0.618 -0.618 1.618
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 -1.618 0.618 0.618 -1.618 12 -1.618 0.618 0.618 -1.618 12 -1.618 0.618 0.618 -1.618 12 -1.618 0.618 0.618 -1.618
12 13 1.618 -0.618 -0.618 1.618 13 1.618 -0.618 -0.618 1.618 13 1.618 -0.618 -0.618 1.618 13 1.618 -0.618 -0.618 1.618
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 -1.618 0.618 0.618 -1.618 17 -1.618 0.618 0.618 -1.618 17 -1.618 0.618 0.618 -1.618 17 -1.618 0.618 0.618 -1.618
17 18 1.618 -0.618 -0.618 1.618 18 1.618 -0.618 -0.618 1.618 18 1.618 -0.618 -0.618 1.618 18 1.618 -0.618 -0.618 1.618
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 0 0 1 0 E8
2 1 0 0 0 0 1 0 0 0 0 0 A⊕E4
3 0 0 0 0 0 1 0 0 0 1 0 E4⊕E8
4 1 0 0 0 0 1 0 0 0 1 0 A⊕E4⊕E8
5 2 0 0 0 0 1 0 0 0 1 0 2A⊕E4⊕E8
6 1 0 0 0 0 1 0 0 0 2 0 A⊕E4⊕2E8
7 2 0 0 0 0 2 0 0 0 1 0 2A⊕2E4⊕E8
8 1 0 0 0 0 2 0 0 0 2 0 A⊕2E4⊕2E8
9 2 0 0 0 0 2 0 0 0 2 0 2A⊕2E4⊕2E8
10 3 0 0 0 0 2 0 0 0 2 0 3A⊕2E4⊕2E8
11 2 0 0 0 0 2 0 0 0 3 0 2A⊕2E4⊕3E8
12 3 0 0 0 0 3 0 0 0 2 0 3A⊕3E4⊕2E8
13 2 0 0 0 0 3 0 0 0 3 0 2A⊕3E4⊕3E8
14 3 0 0 0 0 3 0 0 0 3 0 3A⊕3E4⊕3E8
15 4 0 0 0 0 3 0 0 0 3 0 4A⊕3E4⊕3E8
16 3 0 0 0 0 3 0 0 0 4 0 3A⊕3E4⊕4E8
17 4 0 0 0 0 4 0 0 0 3 0 4A⊕4E4⊕3E8
18 3 0 0 0 0 4 0 0 0 4 0 3A⊕4E4⊕4E8
19 4 0 0 0 0 4 0 0 0 4 0 4A⊕4E4⊕4E8
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