Results for Point Group D20



Symmetric powers of degenerate representation E8
Vibrational overtones


Characters of symmetric powers
Power
To
E 2C20 2C10 2(C20)3 2C5 2C4 2(C10)3 2(C20)7 2(C5)2 2(C20)9 C2 10C'2 10C''2
1 2 -1.618 0.618 0.618 -1.618 2 -1.618 0.618 0.618 -1.618 2 0 0
2 3 1.618 -0.618 -0.618 1.618 3 1.618 -0.618 -0.618 1.618 3 1 1
3 4 -1.000 -1.000 -1.000 -1.000 4 -1.000 -1.000 -1.000 -1.000 4 0 0
4 5 -0.000 0.000 -0.000 0.000 5 0.000 0.000 -0.000 0.000 5 1 1
5 6 1.000 1.000 1.000 1.000 6 1.000 1.000 1.000 1.000 6 0 0
6 7 -1.618 0.618 0.618 -1.618 7 -1.618 0.618 0.618 -1.618 7 1 1
7 8 1.618 -0.618 -0.618 1.618 8 1.618 -0.618 -0.618 1.618 8 0 0
8 9 -1.000 -1.000 -1.000 -1.000 9 -1.000 -1.000 -1.000 -1.000 9 1 1
9 10 -0.000 0.000 -0.000 0.000 10 0.000 0.000 -0.000 0.000 10 0 0
10 11 1.000 1.000 1.000 1.000 11 1.000 1.000 1.000 1.000 11 1 1
11 12 -1.618 0.618 0.618 -1.618 12 -1.618 0.618 0.618 -1.618 12 0 0
12 13 1.618 -0.618 -0.618 1.618 13 1.618 -0.618 -0.618 1.618 13 1 1
13 14 -1.000 -1.000 -1.000 -1.000 14 -1.000 -1.000 -1.000 -1.000 14 0 0
14 15 -0.000 0.000 -0.000 0.000 15 0.000 0.000 -0.000 0.000 15 1 1
15 16 1.000 1.000 1.000 1.000 16 1.000 1.000 1.000 1.000 16 0 0
16 17 -1.618 0.618 0.618 -1.618 17 -1.618 0.618 0.618 -1.618 17 1 1
17 18 1.618 -0.618 -0.618 1.618 18 1.618 -0.618 -0.618 1.618 18 0 0
18 19 -1.000 -1.000 -1.000 -1.000 19 -1.000 -1.000 -1.000 -1.000 19 1 1
19 20 -0.000 0.000 -0.000 0.000 20 0.000 0.000 -0.000 0.000 20 0 0
20 21 1.000 1.000 1.000 1.000 21 1.000 1.000 1.000 1.000 21 1 1


Decomposition to irreducible representations
Power
To
A1 A2 B1 B2 E1 E2 E3 E4 E5 E6 E7 E8 E9
1 0 0 0 0 0 0 0 0 0 0 0 1 0 E8
2 1 0 0 0 0 0 0 1 0 0 0 0 0 A1⊕E4
3 0 0 0 0 0 0 0 1 0 0 0 1 0 E4⊕E8
4 1 0 0 0 0 0 0 1 0 0 0 1 0 A1⊕E4⊕E8
5 1 1 0 0 0 0 0 1 0 0 0 1 0 A1⊕A2⊕E4⊕E8
6 1 0 0 0 0 0 0 1 0 0 0 2 0 A1⊕E4⊕2E8
7 1 1 0 0 0 0 0 2 0 0 0 1 0 A1⊕A2⊕2E4⊕E8
8 1 0 0 0 0 0 0 2 0 0 0 2 0 A1⊕2E4⊕2E8
9 1 1 0 0 0 0 0 2 0 0 0 2 0 A1⊕A2⊕2E4⊕2E8
10 2 1 0 0 0 0 0 2 0 0 0 2 0 2A1⊕A2⊕2E4⊕2E8
11 1 1 0 0 0 0 0 2 0 0 0 3 0 A1⊕A2⊕2E4⊕3E8
12 2 1 0 0 0 0 0 3 0 0 0 2 0 2A1⊕A2⊕3E4⊕2E8
13 1 1 0 0 0 0 0 3 0 0 0 3 0 A1⊕A2⊕3E4⊕3E8
14 2 1 0 0 0 0 0 3 0 0 0 3 0 2A1⊕A2⊕3E4⊕3E8
15 2 2 0 0 0 0 0 3 0 0 0 3 0 2A1⊕2A2⊕3E4⊕3E8
16 2 1 0 0 0 0 0 3 0 0 0 4 0 2A1⊕A2⊕3E4⊕4E8
17 2 2 0 0 0 0 0 4 0 0 0 3 0 2A1⊕2A2⊕4E4⊕3E8
18 2 1 0 0 0 0 0 4 0 0 0 4 0 2A1⊕A2⊕4E4⊕4E8
19 2 2 0 0 0 0 0 4 0 0 0 4 0 2A1⊕2A2⊕4E4⊕4E8
20 3 2 0 0 0 0 0 4 0 0 0 4 0 3A1⊕2A2⊕4E4⊕4E8



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