Results for Point Group D15



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 15C'2
1 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 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 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 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 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 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 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 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 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 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


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



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