Results for Point Group C10



Symmetric powers of degenerate representation E4
Vibrational overtones


Characters of symmetric powers
Power
To
E C10 C5 (C10)3 (C5)2 C2 (C5)3 (C10)7 (C5)4 (C10)9
1 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 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 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 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 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 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 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 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 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 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


Decomposition to irreducible representations
Power
To
A B E1* E2* E3* E4*
1 0 0 0 0 0 1 E4
2 1 0 0 1 0 0 A⊕E2
3 0 0 0 1 0 1 E2⊕E4
4 1 0 0 1 0 1 A⊕E2⊕E4
5 2 0 0 1 0 1 2A⊕E2⊕E4
6 1 0 0 1 0 2 A⊕E2⊕2E4
7 2 0 0 2 0 1 2A⊕2E2⊕E4
8 1 0 0 2 0 2 A⊕2E2⊕2E4
9 2 0 0 2 0 2 2A⊕2E2⊕2E4
10 3 0 0 2 0 2 3A⊕2E2⊕2E4
11 2 0 0 2 0 3 2A⊕2E2⊕3E4
12 3 0 0 3 0 2 3A⊕3E2⊕2E4
13 2 0 0 3 0 3 2A⊕3E2⊕3E4
14 3 0 0 3 0 3 3A⊕3E2⊕3E4
15 4 0 0 3 0 3 4A⊕3E2⊕3E4
16 3 0 0 3 0 4 3A⊕3E2⊕4E4
17 4 0 0 4 0 3 4A⊕4E2⊕3E4
18 3 0 0 4 0 4 3A⊕4E2⊕4E4
19 4 0 0 4 0 4 4A⊕4E2⊕4E4
20 5 0 0 4 0 4 5A⊕4E2⊕4E4



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