Results for Point Group D10



Symmetric powers of degenerate representation E3
Vibrational overtones


Characters of symmetric powers
Power
To
E 2C10 2C5 2(C10)3 2(C5)2 C2 5C'2 5C''2
1 2 -0.618 -1.618 1.618 0.618 -2 0 0
2 3 -0.618 1.618 1.618 -0.618 3 1 1
3 4 1.000 -1.000 1.000 -1.000 -4 0 0
4 5 0.000 0.000 0.000 -0.000 5 1 1
5 6 -1.000 1.000 -1.000 1.000 -6 0 0
6 7 0.618 -1.618 -1.618 0.618 7 1 1
7 8 0.618 1.618 -1.618 -0.618 -8 0 0
8 9 -1.000 -1.000 -1.000 -1.000 9 1 1
9 10 -0.000 0.000 -0.000 -0.000 -10 0 0
10 11 1.000 1.000 1.000 1.000 11 1 1
11 12 -0.618 -1.618 1.618 0.618 -12 0 0
12 13 -0.618 1.618 1.618 -0.618 13 1 1
13 14 1.000 -1.000 1.000 -1.000 -14 0 0
14 15 0.000 0.000 0.000 -0.000 15 1 1
15 16 -1.000 1.000 -1.000 1.000 -16 0 0
16 17 0.618 -1.618 -1.618 0.618 17 1 1
17 18 0.618 1.618 -1.618 -0.618 -18 0 0
18 19 -1.000 -1.000 -1.000 -1.000 19 1 1
19 20 -0.000 0.000 -0.000 -0.000 -20 0 0
20 21 1.000 1.000 1.000 1.000 21 1 1


Decomposition to irreducible representations
Power
To
A1 A2 B1 B2 E1 E2 E3 E4
1 0 0 0 0 0 0 1 0 E3
2 1 0 0 0 0 0 0 1 A1⊕E4
3 0 0 0 0 1 0 1 0 E1⊕E3
4 1 0 0 0 0 1 0 1 A1⊕E2⊕E4
5 0 0 1 1 1 0 1 0 B1⊕B2⊕E1⊕E3
6 1 0 0 0 0 2 0 1 A1⊕2E2⊕E4
7 0 0 1 1 2 0 1 0 B1⊕B2⊕2E1⊕E3
8 1 0 0 0 0 2 0 2 A1⊕2E2⊕2E4
9 0 0 1 1 2 0 2 0 B1⊕B2⊕2E1⊕2E3
10 2 1 0 0 0 2 0 2 2A1⊕A2⊕2E2⊕2E4
11 0 0 1 1 2 0 3 0 B1⊕B2⊕2E1⊕3E3
12 2 1 0 0 0 2 0 3 2A1⊕A2⊕2E2⊕3E4
13 0 0 1 1 3 0 3 0 B1⊕B2⊕3E1⊕3E3
14 2 1 0 0 0 3 0 3 2A1⊕A2⊕3E2⊕3E4
15 0 0 2 2 3 0 3 0 2B1⊕2B2⊕3E1⊕3E3
16 2 1 0 0 0 4 0 3 2A1⊕A2⊕4E2⊕3E4
17 0 0 2 2 4 0 3 0 2B1⊕2B2⊕4E1⊕3E3
18 2 1 0 0 0 4 0 4 2A1⊕A2⊕4E2⊕4E4
19 0 0 2 2 4 0 4 0 2B1⊕2B2⊕4E1⊕4E3
20 3 2 0 0 0 4 0 4 3A1⊕2A2⊕4E2⊕4E4



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