Results for Point Group C10



Symmetric powers of degenerate representation E3
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 -0.618 -1.618 1.618 0.618 -2 0.618 1.618 -1.618 -0.618
2 3 -0.618 1.618 1.618 -0.618 3 -0.618 1.618 1.618 -0.618
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 0.618 -1.618 -1.618 0.618 7 0.618 -1.618 -1.618 0.618
7 8 0.618 1.618 -1.618 -0.618 -8 -0.618 -1.618 1.618 0.618
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 -0.618 -1.618 1.618 0.618 -12 0.618 1.618 -1.618 -0.618
12 13 -0.618 1.618 1.618 -0.618 13 -0.618 1.618 1.618 -0.618
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 0.618 -1.618 -1.618 0.618 17 0.618 -1.618 -1.618 0.618
17 18 0.618 1.618 -1.618 -0.618 -18 -0.618 -1.618 1.618 0.618
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 1 0 E3
2 1 0 0 0 0 1 A⊕E4
3 0 0 1 0 1 0 E1⊕E3
4 1 0 0 1 0 1 A⊕E2⊕E4
5 0 2 1 0 1 0 2B⊕E1⊕E3
6 1 0 0 2 0 1 A⊕2E2⊕E4
7 0 2 2 0 1 0 2B⊕2E1⊕E3
8 1 0 0 2 0 2 A⊕2E2⊕2E4
9 0 2 2 0 2 0 2B⊕2E1⊕2E3
10 3 0 0 2 0 2 3A⊕2E2⊕2E4
11 0 2 2 0 3 0 2B⊕2E1⊕3E3
12 3 0 0 2 0 3 3A⊕2E2⊕3E4
13 0 2 3 0 3 0 2B⊕3E1⊕3E3
14 3 0 0 3 0 3 3A⊕3E2⊕3E4
15 0 4 3 0 3 0 4B⊕3E1⊕3E3
16 3 0 0 4 0 3 3A⊕4E2⊕3E4
17 0 4 4 0 3 0 4B⊕4E1⊕3E3
18 3 0 0 4 0 4 3A⊕4E2⊕4E4
19 0 4 4 0 4 0 4B⊕4E1⊕4E3
20 5 0 0 4 0 4 5A⊕4E2⊕4E4



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