Results for Point Group D15d



Symmetric powers of degenerate representation E3g
Vibrational overtones


Characters of symmetric powers
Power
To
E 2C15 2(C15)2 2C5 2(C15)4 2C3 2(C5)2 2(C15)7 15C'2 i 2(S30)13 2(S30)11 2(S10)3 2(S30)7 2S6 2S10 2S30 15σd
1 2 0.618 -1.618 -1.618 0.618 2 0.618 -1.618 0 2 0.618 -1.618 -1.618 0.618 2 0.618 -1.618 0
2 3 -0.618 1.618 1.618 -0.618 3 -0.618 1.618 1 3 -0.618 1.618 1.618 -0.618 3 -0.618 1.618 1
3 4 -1.000 -1.000 -1.000 -1.000 4 -1.000 -1.000 0 4 -1.000 -1.000 -1.000 -1.000 4 -1.000 -1.000 0
4 5 -0.000 -0.000 0.000 0.000 5 -0.000 -0.000 1 5 -0.000 -0.000 0.000 0.000 5 -0.000 -0.000 1
5 6 1.000 1.000 1.000 1.000 6 1.000 1.000 0 6 1.000 1.000 1.000 1.000 6 1.000 1.000 0
6 7 0.618 -1.618 -1.618 0.618 7 0.618 -1.618 1 7 0.618 -1.618 -1.618 0.618 7 0.618 -1.618 1
7 8 -0.618 1.618 1.618 -0.618 8 -0.618 1.618 0 8 -0.618 1.618 1.618 -0.618 8 -0.618 1.618 0
8 9 -1.000 -1.000 -1.000 -1.000 9 -1.000 -1.000 1 9 -1.000 -1.000 -1.000 -1.000 9 -1.000 -1.000 1
9 10 -0.000 -0.000 0.000 0.000 10 -0.000 -0.000 0 10 -0.000 -0.000 0.000 0.000 10 -0.000 -0.000 0
10 11 1.000 1.000 1.000 1.000 11 1.000 1.000 1 11 1.000 1.000 1.000 1.000 11 1.000 1.000 1
11 12 0.618 -1.618 -1.618 0.618 12 0.618 -1.618 0 12 0.618 -1.618 -1.618 0.618 12 0.618 -1.618 0
12 13 -0.618 1.618 1.618 -0.618 13 -0.618 1.618 1 13 -0.618 1.618 1.618 -0.618 13 -0.618 1.618 1
13 14 -1.000 -1.000 -1.000 -1.000 14 -1.000 -1.000 0 14 -1.000 -1.000 -1.000 -1.000 14 -1.000 -1.000 0
14 15 -0.000 -0.000 0.000 0.000 15 -0.000 -0.000 1 15 -0.000 -0.000 0.000 0.000 15 -0.000 -0.000 1
15 16 1.000 1.000 1.000 1.000 16 1.000 1.000 0 16 1.000 1.000 1.000 1.000 16 1.000 1.000 0
16 17 0.618 -1.618 -1.618 0.618 17 0.618 -1.618 1 17 0.618 -1.618 -1.618 0.618 17 0.618 -1.618 1
17 18 -0.618 1.618 1.618 -0.618 18 -0.618 1.618 0 18 -0.618 1.618 1.618 -0.618 18 -0.618 1.618 0
18 19 -1.000 -1.000 -1.000 -1.000 19 -1.000 -1.000 1 19 -1.000 -1.000 -1.000 -1.000 19 -1.000 -1.000 1
19 20 -0.000 -0.000 0.000 0.000 20 -0.000 -0.000 0 20 -0.000 -0.000 0.000 0.000 20 -0.000 -0.000 0
20 21 1.000 1.000 1.000 1.000 21 1.000 1.000 1 21 1.000 1.000 1.000 1.000 21 1.000 1.000 1


Decomposition to irreducible representations
Power
To
A1g A2g E1g E2g E3g E4g E5g E6g E7g A1u A2u E1u E2u E3u E4u E5u E6u E7u
1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 E3g
2 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 A1g⊕E6g
3 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 E3g⊕E6g
4 1 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 A1g⊕E3g⊕E6g
5 1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 A1g⊕A2g⊕E3g⊕E6g
6 1 0 0 0 2 0 0 1 0 0 0 0 0 0 0 0 0 0 A1g⊕2E3g⊕E6g
7 1 1 0 0 1 0 0 2 0 0 0 0 0 0 0 0 0 0 A1g⊕A2g⊕E3g⊕2E6g
8 1 0 0 0 2 0 0 2 0 0 0 0 0 0 0 0 0 0 A1g⊕2E3g⊕2E6g
9 1 1 0 0 2 0 0 2 0 0 0 0 0 0 0 0 0 0 A1g⊕A2g⊕2E3g⊕2E6g
10 2 1 0 0 2 0 0 2 0 0 0 0 0 0 0 0 0 0 2A1g⊕A2g⊕2E3g⊕2E6g
11 1 1 0 0 3 0 0 2 0 0 0 0 0 0 0 0 0 0 A1g⊕A2g⊕3E3g⊕2E6g
12 2 1 0 0 2 0 0 3 0 0 0 0 0 0 0 0 0 0 2A1g⊕A2g⊕2E3g⊕3E6g
13 1 1 0 0 3 0 0 3 0 0 0 0 0 0 0 0 0 0 A1g⊕A2g⊕3E3g⊕3E6g
14 2 1 0 0 3 0 0 3 0 0 0 0 0 0 0 0 0 0 2A1g⊕A2g⊕3E3g⊕3E6g
15 2 2 0 0 3 0 0 3 0 0 0 0 0 0 0 0 0 0 2A1g⊕2A2g⊕3E3g⊕3E6g
16 2 1 0 0 4 0 0 3 0 0 0 0 0 0 0 0 0 0 2A1g⊕A2g⊕4E3g⊕3E6g
17 2 2 0 0 3 0 0 4 0 0 0 0 0 0 0 0 0 0 2A1g⊕2A2g⊕3E3g⊕4E6g
18 2 1 0 0 4 0 0 4 0 0 0 0 0 0 0 0 0 0 2A1g⊕A2g⊕4E3g⊕4E6g
19 2 2 0 0 4 0 0 4 0 0 0 0 0 0 0 0 0 0 2A1g⊕2A2g⊕4E3g⊕4E6g
20 3 2 0 0 4 0 0 4 0 0 0 0 0 0 0 0 0 0 3A1g⊕2A2g⊕4E3g⊕4E6g



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