Results for Point Group D18



Symmetric powers of degenerate representation E3
Vibrational overtones


Characters of symmetric powers
Power
To
E 2C18 2C9 2C6 2(C9)2 2(C18)5 2C3 2(C18)7 2(C9)4 C2 9C'2 9C''2
1 2 1.000 -1.000 -2 -1.000 1.000 2 1.000 -1.000 -2 0 0
2 3 0.000 0.000 3 0.000 0.000 3 0.000 0.000 3 1 1
3 4 -1.000 1.000 -4 1.000 -1.000 4 -1.000 1.000 -4 0 0
4 5 -1.000 -1.000 5 -1.000 -1.000 5 -1.000 -1.000 5 1 1
5 6 0.000 0.000 -6 0.000 0.000 6 0.000 0.000 -6 0 0
6 7 1.000 1.000 7 1.000 1.000 7 1.000 1.000 7 1 1
7 8 1.000 -1.000 -8 -1.000 1.000 8 1.000 -1.000 -8 0 0
8 9 0.000 0.000 9 0.000 0.000 9 0.000 0.000 9 1 1
9 10 -1.000 1.000 -10 1.000 -1.000 10 -1.000 1.000 -10 0 0
10 11 -1.000 -1.000 11 -1.000 -1.000 11 -1.000 -1.000 11 1 1
11 12 0.000 0.000 -12 0.000 0.000 12 0.000 0.000 -12 0 0
12 13 1.000 1.000 13 1.000 1.000 13 1.000 1.000 13 1 1
13 14 1.000 -1.000 -14 -1.000 1.000 14 1.000 -1.000 -14 0 0
14 15 0.000 0.000 15 0.000 0.000 15 0.000 0.000 15 1 1
15 16 -1.000 1.000 -16 1.000 -1.000 16 -1.000 1.000 -16 0 0
16 17 -1.000 -1.000 17 -1.000 -1.000 17 -1.000 -1.000 17 1 1
17 18 0.000 0.000 -18 0.000 0.000 18 0.000 0.000 -18 0 0
18 19 1.000 1.000 19 1.000 1.000 19 1.000 1.000 19 1 1
19 20 1.000 -1.000 -20 -1.000 1.000 20 1.000 -1.000 -20 0 0
20 21 0.000 0.000 21 0.000 0.000 21 0.000 0.000 21 1 1


Decomposition to irreducible representations
Power
To
A1 A2 B1 B2 E1 E2 E3 E4 E5 E6 E7 E8
1 0 0 0 0 0 0 1 0 0 0 0 0 E3
2 1 0 0 0 0 0 0 0 0 1 0 0 A1⊕E6
3 0 0 1 1 0 0 1 0 0 0 0 0 B1⊕B2⊕E3
4 1 0 0 0 0 0 0 0 0 2 0 0 A1⊕2E6
5 0 0 1 1 0 0 2 0 0 0 0 0 B1⊕B2⊕2E3
6 2 1 0 0 0 0 0 0 0 2 0 0 2A1⊕A2⊕2E6
7 0 0 1 1 0 0 3 0 0 0 0 0 B1⊕B2⊕3E3
8 2 1 0 0 0 0 0 0 0 3 0 0 2A1⊕A2⊕3E6
9 0 0 2 2 0 0 3 0 0 0 0 0 2B1⊕2B2⊕3E3
10 2 1 0 0 0 0 0 0 0 4 0 0 2A1⊕A2⊕4E6
11 0 0 2 2 0 0 4 0 0 0 0 0 2B1⊕2B2⊕4E3
12 3 2 0 0 0 0 0 0 0 4 0 0 3A1⊕2A2⊕4E6
13 0 0 2 2 0 0 5 0 0 0 0 0 2B1⊕2B2⊕5E3
14 3 2 0 0 0 0 0 0 0 5 0 0 3A1⊕2A2⊕5E6
15 0 0 3 3 0 0 5 0 0 0 0 0 3B1⊕3B2⊕5E3
16 3 2 0 0 0 0 0 0 0 6 0 0 3A1⊕2A2⊕6E6
17 0 0 3 3 0 0 6 0 0 0 0 0 3B1⊕3B2⊕6E3
18 4 3 0 0 0 0 0 0 0 6 0 0 4A1⊕3A2⊕6E6
19 0 0 3 3 0 0 7 0 0 0 0 0 3B1⊕3B2⊕7E3
20 4 3 0 0 0 0 0 0 0 7 0 0 4A1⊕3A2⊕7E6



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