Results for Point Group C15



Symmetric powers of degenerate representation E3
Vibrational overtones


Characters of symmetric powers
Power
To
E 2C15 2(C15)2 2C5 2(C15)4 2C3 2(C5)2 2(C15)7
1 2 0.618 -1.618 -1.618 0.618 2 0.618 -1.618
2 3 -0.618 1.618 1.618 -0.618 3 -0.618 1.618
3 4 -1.000 -1.000 -1.000 -1.000 4 -1.000 -1.000
4 5 -0.000 -0.000 0.000 0.000 5 -0.000 -0.000
5 6 1.000 1.000 1.000 1.000 6 1.000 1.000
6 7 0.618 -1.618 -1.618 0.618 7 0.618 -1.618
7 8 -0.618 1.618 1.618 -0.618 8 -0.618 1.618
8 9 -1.000 -1.000 -1.000 -1.000 9 -1.000 -1.000
9 10 -0.000 -0.000 0.000 0.000 10 -0.000 -0.000
10 11 1.000 1.000 1.000 1.000 11 1.000 1.000
11 12 0.618 -1.618 -1.618 0.618 12 0.618 -1.618
12 13 -0.618 1.618 1.618 -0.618 13 -0.618 1.618
13 14 -1.000 -1.000 -1.000 -1.000 14 -1.000 -1.000
14 15 -0.000 -0.000 0.000 0.000 15 -0.000 -0.000
15 16 1.000 1.000 1.000 1.000 16 1.000 1.000
16 17 0.618 -1.618 -1.618 0.618 17 0.618 -1.618
17 18 -0.618 1.618 1.618 -0.618 18 -0.618 1.618
18 19 -1.000 -1.000 -1.000 -1.000 19 -1.000 -1.000
19 20 -0.000 -0.000 0.000 0.000 20 -0.000 -0.000
20 21 1.000 1.000 1.000 1.000 21 1.000 1.000


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



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