Results for Point Group D18



Symmetric powers of degenerate representation E8
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 -1.879 1.532 -1 0.347 0.347 -1 1.532 -1.879 2 0 0
2 3 2.532 1.347 0 -0.879 -0.879 0 1.347 2.532 3 1 1
3 4 -2.879 0.532 1 -0.653 -0.653 1 0.532 -2.879 4 0 0
4 5 2.879 -0.532 -1 0.653 0.653 -1 -0.532 2.879 5 1 1
5 6 -2.532 -1.347 0 0.879 0.879 0 -1.347 -2.532 6 0 0
6 7 1.879 -1.532 1 -0.347 -0.347 1 -1.532 1.879 7 1 1
7 8 -1.000 -1.000 -1 -1.000 -1.000 -1 -1.000 -1.000 8 0 0
8 9 -0.000 0.000 0 0.000 -0.000 0 -0.000 0.000 9 1 1
9 10 1.000 1.000 1 1.000 1.000 1 1.000 1.000 10 0 0
10 11 -1.879 1.532 -1 0.347 0.347 -1 1.532 -1.879 11 1 1
11 12 2.532 1.347 0 -0.879 -0.879 0 1.347 2.532 12 0 0
12 13 -2.879 0.532 1 -0.653 -0.653 1 0.532 -2.879 13 1 1
13 14 2.879 -0.532 -1 0.653 0.653 -1 -0.532 2.879 14 0 0
14 15 -2.532 -1.347 0 0.879 0.879 0 -1.347 -2.532 15 1 1
15 16 1.879 -1.532 1 -0.347 -0.347 1 -1.532 1.879 16 0 0
16 17 -1.000 -1.000 -1 -1.000 -1.000 -1 -1.000 -1.000 17 1 1
17 18 -0.000 0.000 0 0.000 -0.000 0 -0.000 0.000 18 0 0
18 19 1.000 1.000 1 1.000 1.000 1 1.000 1.000 19 1 1
19 20 -1.879 1.532 -1 0.347 0.347 -1 1.532 -1.879 20 0 0
20 21 2.532 1.347 0 -0.879 -0.879 0 1.347 2.532 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 0 0 0 0 0 1 E8
2 1 0 0 0 0 1 0 0 0 0 0 0 A1⊕E2
3 0 0 0 0 0 0 0 0 0 1 0 1 E6⊕E8
4 1 0 0 0 0 1 0 1 0 0 0 0 A1⊕E2⊕E4
5 0 0 0 0 0 0 0 1 0 1 0 1 E4⊕E6⊕E8
6 1 0 0 0 0 1 0 1 0 1 0 0 A1⊕E2⊕E4⊕E6
7 0 0 0 0 0 1 0 1 0 1 0 1 E2⊕E4⊕E6⊕E8
8 1 0 0 0 0 1 0 1 0 1 0 1 A1⊕E2⊕E4⊕E6⊕E8
9 1 1 0 0 0 1 0 1 0 1 0 1 A1⊕A2⊕E2⊕E4⊕E6⊕E8
10 1 0 0 0 0 1 0 1 0 1 0 2 A1⊕E2⊕E4⊕E6⊕2E8
11 1 1 0 0 0 2 0 1 0 1 0 1 A1⊕A2⊕2E2⊕E4⊕E6⊕E8
12 1 0 0 0 0 1 0 1 0 2 0 2 A1⊕E2⊕E4⊕2E6⊕2E8
13 1 1 0 0 0 2 0 2 0 1 0 1 A1⊕A2⊕2E2⊕2E4⊕E6⊕E8
14 1 0 0 0 0 1 0 2 0 2 0 2 A1⊕E2⊕2E4⊕2E6⊕2E8
15 1 1 0 0 0 2 0 2 0 2 0 1 A1⊕A2⊕2E2⊕2E4⊕2E6⊕E8
16 1 0 0 0 0 2 0 2 0 2 0 2 A1⊕2E2⊕2E4⊕2E6⊕2E8
17 1 1 0 0 0 2 0 2 0 2 0 2 A1⊕A2⊕2E2⊕2E4⊕2E6⊕2E8
18 2 1 0 0 0 2 0 2 0 2 0 2 2A1⊕A2⊕2E2⊕2E4⊕2E6⊕2E8
19 1 1 0 0 0 2 0 2 0 2 0 3 A1⊕A2⊕2E2⊕2E4⊕2E6⊕3E8
20 2 1 0 0 0 3 0 2 0 2 0 2 2A1⊕A2⊕3E2⊕2E4⊕2E6⊕2E8



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