Results for Point Group S20



Symmetric powers of degenerate representation E9
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 -1.902 1.618 -1.176 0.618 0 -0.618 1.176 -1.618 1.902 -2 1.902 -1.618 1.176 -0.618 0 0.618 -1.176 1.618 -1.902
2 3 2.618 1.618 0.382 -0.618 -1 -0.618 0.382 1.618 2.618 3 2.618 1.618 0.382 -0.618 -1 -0.618 0.382 1.618 2.618
3 4 -3.078 1.000 0.727 -1.000 0 1.000 -0.727 -1.000 3.078 -4 3.078 -1.000 -0.727 1.000 0 -1.000 0.727 1.000 -3.078
4 5 3.236 -0.000 -1.236 0.000 1 -0.000 -1.236 0.000 3.236 5 3.236 -0.000 -1.236 -0.000 1 -0.000 -1.236 0.000 3.236
5 6 -3.078 -1.000 0.727 1.000 0 -1.000 -0.727 1.000 3.078 -6 3.078 1.000 -0.727 -1.000 0 1.000 0.727 -1.000 -3.078
6 7 2.618 -1.618 0.382 0.618 -1 0.618 0.382 -1.618 2.618 7 2.618 -1.618 0.382 0.618 -1 0.618 0.382 -1.618 2.618
7 8 -1.902 -1.618 -1.176 -0.618 0 0.618 1.176 1.618 1.902 -8 1.902 1.618 1.176 0.618 0 -0.618 -1.176 -1.618 -1.902
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 1.902 1.618 1.176 0.618 0 -0.618 -1.176 -1.618 -1.902 -12 -1.902 -1.618 -1.176 -0.618 0 0.618 1.176 1.618 1.902
12 13 -2.618 1.618 -0.382 -0.618 1 -0.618 -0.382 1.618 -2.618 13 -2.618 1.618 -0.382 -0.618 1 -0.618 -0.382 1.618 -2.618
13 14 3.078 1.000 -0.727 -1.000 0 1.000 0.727 -1.000 -3.078 -14 -3.078 -1.000 0.727 1.000 0 -1.000 -0.727 1.000 3.078
14 15 -3.236 -0.000 1.236 0.000 -1 -0.000 1.236 0.000 -3.236 15 -3.236 -0.000 1.236 -0.000 -1 -0.000 1.236 0.000 -3.236
15 16 3.078 -1.000 -0.727 1.000 0 -1.000 0.727 1.000 -3.078 -16 -3.078 1.000 0.727 -1.000 0 1.000 -0.727 -1.000 3.078
16 17 -2.618 -1.618 -0.382 0.618 1 0.618 -0.382 -1.618 -2.618 17 -2.618 -1.618 -0.382 0.618 1 0.618 -0.382 -1.618 -2.618
17 18 1.902 -1.618 1.176 -0.618 0 0.618 -1.176 1.618 -1.902 -18 -1.902 1.618 -1.176 0.618 0 -0.618 1.176 -1.618 1.902
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 0 0 1 E9
2 1 0 0 1 0 0 0 0 0 0 0 A⊕E2
3 0 0 0 0 0 0 0 0 1 0 1 E7⊕E9
4 1 0 0 1 0 1 0 0 0 0 0 A⊕E2⊕E4
5 0 0 0 0 0 0 1 0 1 0 1 E5⊕E7⊕E9
6 1 0 0 1 0 1 0 1 0 0 0 A⊕E2⊕E4⊕E6
7 0 0 0 0 1 0 1 0 1 0 1 E3⊕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 2 0 1 0 1 0 1 0 1 2E1⊕E3⊕E5⊕E7⊕E9
12 1 2 0 1 0 1 0 1 0 2 0 A⊕2B⊕E2⊕E4⊕E6⊕2E8
13 0 0 2 0 2 0 1 0 1 0 1 2E1⊕2E3⊕E5⊕E7⊕E9
14 1 2 0 1 0 1 0 2 0 2 0 A⊕2B⊕E2⊕E4⊕2E6⊕2E8
15 0 0 2 0 2 0 2 0 1 0 1 2E1⊕2E3⊕2E5⊕E7⊕E9
16 1 2 0 1 0 2 0 2 0 2 0 A⊕2B⊕E2⊕2E4⊕2E6⊕2E8
17 0 0 2 0 2 0 2 0 2 0 1 2E1⊕2E3⊕2E5⊕2E7⊕E9
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 November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement