Results for Point Group S20



Symmetric powers of degenerate representation E2
Vibrational overtones


Characters of symmetric powers
Power
To
E 2S20 2C10 2(S20)3 2C5 2S4 2(C10)3 2(S20)7 2(C5)2 2(S20)9 C2
1 2 1.618 0.618 -0.618 -1.618 -2 -1.618 -0.618 0.618 1.618 2
2 3 1.618 -0.618 -0.618 1.618 3 1.618 -0.618 -0.618 1.618 3
3 4 1.000 -1.000 1.000 -1.000 -4 -1.000 1.000 -1.000 1.000 4
4 5 0.000 -0.000 0.000 -0.000 5 0.000 -0.000 0.000 -0.000 5
5 6 -1.000 1.000 -1.000 1.000 -6 1.000 -1.000 1.000 -1.000 6
6 7 -1.618 0.618 0.618 -1.618 7 -1.618 0.618 0.618 -1.618 7
7 8 -1.618 -0.618 0.618 1.618 -8 1.618 0.618 -0.618 -1.618 8
8 9 -1.000 -1.000 -1.000 -1.000 9 -1.000 -1.000 -1.000 -1.000 9
9 10 -0.000 -0.000 -0.000 -0.000 -10 0.000 0.000 0.000 0.000 10
10 11 1.000 1.000 1.000 1.000 11 1.000 1.000 1.000 1.000 11
11 12 1.618 0.618 -0.618 -1.618 -12 -1.618 -0.618 0.618 1.618 12
12 13 1.618 -0.618 -0.618 1.618 13 1.618 -0.618 -0.618 1.618 13
13 14 1.000 -1.000 1.000 -1.000 -14 -1.000 1.000 -1.000 1.000 14
14 15 0.000 -0.000 0.000 -0.000 15 0.000 -0.000 0.000 -0.000 15
15 16 -1.000 1.000 -1.000 1.000 -16 1.000 -1.000 1.000 -1.000 16
16 17 -1.618 0.618 0.618 -1.618 17 -1.618 0.618 0.618 -1.618 17
17 18 -1.618 -0.618 0.618 1.618 -18 1.618 0.618 -0.618 -1.618 18
18 19 -1.000 -1.000 -1.000 -1.000 19 -1.000 -1.000 -1.000 -1.000 19
19 20 -0.000 -0.000 -0.000 -0.000 -20 0.000 0.000 0.000 0.000 20
20 21 1.000 1.000 1.000 1.000 21 1.000 1.000 1.000 1.000 21


Decomposition to irreducible representations
Power
To
A B E1* E2* E3* E4* E5* E6* E7* E8* E9*
1 0 0 0 1 0 0 0 0 0 0 0 E2
2 1 0 0 0 0 1 0 0 0 0 0 A⊕E4
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 1 0 0 0 2 0 A⊕E4⊕2E8
7 0 2 0 1 0 0 0 2 0 0 0 2B⊕E2⊕2E6
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 3 0 0 0 2 0 0 0 2B⊕3E2⊕2E6
12 3 0 0 0 0 3 0 0 0 2 0 3A⊕3E4⊕2E8
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 3 0 0 0 4 0 3A⊕3E4⊕4E8
17 0 4 0 3 0 0 0 4 0 0 0 4B⊕3E2⊕4E6
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 January, 3rd 2020 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement