Results for Point Group C20



Symmetric powers of degenerate representation E7
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 -1.176 -0.618 1.902 -1.618 0 1.618 -1.902 0.618 1.176 -2 1.176 0.618 -1.902 1.618 0 -1.618 1.902 -0.618 -1.176
2 3 0.382 -0.618 2.618 1.618 -1 1.618 2.618 -0.618 0.382 3 0.382 -0.618 2.618 1.618 -1 1.618 2.618 -0.618 0.382
3 4 0.727 1.000 3.078 -1.000 0 1.000 -3.078 -1.000 -0.727 -4 -0.727 -1.000 -3.078 1.000 0 -1.000 3.078 1.000 0.727
4 5 -1.236 -0.000 3.236 -0.000 1 0.000 3.236 0.000 -1.236 5 -1.236 -0.000 3.236 -0.000 1 0.000 3.236 -0.000 -1.236
5 6 0.727 -1.000 3.078 1.000 0 -1.000 -3.078 1.000 -0.727 -6 -0.727 1.000 -3.078 -1.000 0 1.000 3.078 -1.000 0.727
6 7 0.382 0.618 2.618 -1.618 -1 -1.618 2.618 0.618 0.382 7 0.382 0.618 2.618 -1.618 -1 -1.618 2.618 0.618 0.382
7 8 -1.176 0.618 1.902 1.618 0 -1.618 -1.902 -0.618 1.176 -8 1.176 -0.618 -1.902 -1.618 0 1.618 1.902 0.618 -1.176
8 9 1.000 -1.000 1.000 -1.000 1 -1.000 1.000 -1.000 1.000 9 1.000 -1.000 1.000 -1.000 1 -1.000 1.000 -1.000 1.000
9 10 0.000 0.000 -0.000 -0.000 0 -0.000 0.000 0.000 -0.000 -10 0.000 -0.000 -0.000 0.000 0 0.000 -0.000 0.000 0.000
10 11 -1.000 1.000 -1.000 1.000 -1 1.000 -1.000 1.000 -1.000 11 -1.000 1.000 -1.000 1.000 -1 1.000 -1.000 1.000 -1.000
11 12 1.176 -0.618 -1.902 -1.618 0 1.618 1.902 0.618 -1.176 -12 -1.176 0.618 1.902 1.618 0 -1.618 -1.902 -0.618 1.176
12 13 -0.382 -0.618 -2.618 1.618 1 1.618 -2.618 -0.618 -0.382 13 -0.382 -0.618 -2.618 1.618 1 1.618 -2.618 -0.618 -0.382
13 14 -0.727 1.000 -3.078 -1.000 0 1.000 3.078 -1.000 0.727 -14 0.727 -1.000 3.078 1.000 0 -1.000 -3.078 1.000 -0.727
14 15 1.236 -0.000 -3.236 -0.000 -1 0.000 -3.236 0.000 1.236 15 1.236 -0.000 -3.236 -0.000 -1 0.000 -3.236 -0.000 1.236
15 16 -0.727 -1.000 -3.078 1.000 0 -1.000 3.078 1.000 0.727 -16 0.727 1.000 3.078 -1.000 0 1.000 -3.078 -1.000 -0.727
16 17 -0.382 0.618 -2.618 -1.618 1 -1.618 -2.618 0.618 -0.382 17 -0.382 0.618 -2.618 -1.618 1 -1.618 -2.618 0.618 -0.382
17 18 1.176 0.618 -1.902 1.618 0 -1.618 1.902 -0.618 -1.176 -18 -1.176 -0.618 1.902 -1.618 0 1.618 -1.902 0.618 1.176
18 19 -1.000 -1.000 -1.000 -1.000 -1 -1.000 -1.000 -1.000 -1.000 19 -1.000 -1.000 -1.000 -1.000 -1 -1.000 -1.000 -1.000 -1.000
19 20 -0.000 0.000 -0.000 -0.000 0 -0.000 -0.000 0.000 0.000 -20 -0.000 -0.000 0.000 0.000 0 0.000 0.000 0.000 -0.000
20 21 1.000 1.000 1.000 1.000 1 1.000 1.000 1.000 1.000 21 1.000 1.000 1.000 1.000 1 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 1 0 0 E7
2 1 0 0 0 0 0 0 1 0 0 0 A⊕E6
3 0 0 1 0 0 0 0 0 1 0 0 E1⊕E7
4 1 0 0 0 0 0 0 1 0 1 0 A⊕E6⊕E8
5 0 0 1 0 0 0 1 0 1 0 0 E1⊕E5⊕E7
6 1 0 0 1 0 0 0 1 0 1 0 A⊕E2⊕E6⊕E8
7 0 0 1 0 0 0 1 0 1 0 1 E1⊕E5⊕E7⊕E9
8 1 0 0 1 0 1 0 1 0 1 0 A⊕E2⊕E4⊕E6⊕E8
9 0 0 1 0 1 0 1 0 1 0 1 E1⊕E3⊕E5⊕E7⊕E9
10 1 2 0 1 0 1 0 1 0 1 0 A⊕2B⊕E2⊕E4⊕E6⊕E8
11 0 0 1 0 2 0 1 0 1 0 1 E1⊕2E3⊕E5⊕E7⊕E9
12 1 2 0 1 0 2 0 1 0 1 0 A⊕2B⊕E2⊕2E4⊕E6⊕E8
13 0 0 1 0 2 0 1 0 1 0 2 E1⊕2E3⊕E5⊕E7⊕2E9
14 1 2 0 2 0 2 0 1 0 1 0 A⊕2B⊕2E2⊕2E4⊕E6⊕E8
15 0 0 1 0 2 0 2 0 1 0 2 E1⊕2E3⊕2E5⊕E7⊕2E9
16 1 2 0 2 0 2 0 1 0 2 0 A⊕2B⊕2E2⊕2E4⊕E6⊕2E8
17 0 0 2 0 2 0 2 0 1 0 2 2E1⊕2E3⊕2E5⊕E7⊕2E9
18 1 2 0 2 0 2 0 2 0 2 0 A⊕2B⊕2E2⊕2E4⊕2E6⊕2E8
19 0 0 2 0 2 0 2 0 2 0 2 2E1⊕2E3⊕2E5⊕2E7⊕2E9
20 3 2 0 2 0 2 0 2 0 2 0 3A⊕2B⊕2E2⊕2E4⊕2E6⊕2E8



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