Results for Point Group C18



Symmetric powers of degenerate representation E8
Vibrational overtones


Characters of symmetric powers
Power
To
E C18 C9 C6 (C9)2 (C18)5 C3 (C18)7 (C9)4 C2 (C9)5 (C18)11 (C3)2 (C18)13 (C9)7 (C6)5 (C9)8 (C18)17
1 2 -1.879 1.532 -1 0.347 0.347 -1 1.532 -1.879 2 -1.879 1.532 -1 0.347 0.347 -1 1.532 -1.879
2 3 2.532 1.347 0 -0.879 -0.879 0 1.347 2.532 3 2.532 1.347 0 -0.879 -0.879 0 1.347 2.532
3 4 -2.879 0.532 1 -0.653 -0.653 1 0.532 -2.879 4 -2.879 0.532 1 -0.653 -0.653 1 0.532 -2.879
4 5 2.879 -0.532 -1 0.653 0.653 -1 -0.532 2.879 5 2.879 -0.532 -1 0.653 0.653 -1 -0.532 2.879
5 6 -2.532 -1.347 0 0.879 0.879 0 -1.347 -2.532 6 -2.532 -1.347 0 0.879 0.879 0 -1.347 -2.532
6 7 1.879 -1.532 1 -0.347 -0.347 1 -1.532 1.879 7 1.879 -1.532 1 -0.347 -0.347 1 -1.532 1.879
7 8 -1.000 -1.000 -1 -1.000 -1.000 -1 -1.000 -1.000 8 -1.000 -1.000 -1 -1.000 -1.000 -1 -1.000 -1.000
8 9 -0.000 0.000 0 0.000 -0.000 0 -0.000 0.000 9 -0.000 0.000 0 0.000 -0.000 0 -0.000 0.000
9 10 1.000 1.000 1 1.000 1.000 1 1.000 1.000 10 1.000 1.000 1 1.000 1.000 1 1.000 1.000
10 11 -1.879 1.532 -1 0.347 0.347 -1 1.532 -1.879 11 -1.879 1.532 -1 0.347 0.347 -1 1.532 -1.879
11 12 2.532 1.347 0 -0.879 -0.879 0 1.347 2.532 12 2.532 1.347 0 -0.879 -0.879 0 1.347 2.532
12 13 -2.879 0.532 1 -0.653 -0.653 1 0.532 -2.879 13 -2.879 0.532 1 -0.653 -0.653 1 0.532 -2.879
13 14 2.879 -0.532 -1 0.653 0.653 -1 -0.532 2.879 14 2.879 -0.532 -1 0.653 0.653 -1 -0.532 2.879
14 15 -2.532 -1.347 0 0.879 0.879 0 -1.347 -2.532 15 -2.532 -1.347 0 0.879 0.879 0 -1.347 -2.532
15 16 1.879 -1.532 1 -0.347 -0.347 1 -1.532 1.879 16 1.879 -1.532 1 -0.347 -0.347 1 -1.532 1.879
16 17 -1.000 -1.000 -1 -1.000 -1.000 -1 -1.000 -1.000 17 -1.000 -1.000 -1 -1.000 -1.000 -1 -1.000 -1.000
17 18 -0.000 0.000 0 0.000 -0.000 0 -0.000 0.000 18 -0.000 0.000 0 0.000 -0.000 0 -0.000 0.000
18 19 1.000 1.000 1 1.000 1.000 1 1.000 1.000 19 1.000 1.000 1 1.000 1.000 1 1.000 1.000
19 20 -1.879 1.532 -1 0.347 0.347 -1 1.532 -1.879 20 -1.879 1.532 -1 0.347 0.347 -1 1.532 -1.879
20 21 2.532 1.347 0 -0.879 -0.879 0 1.347 2.532 21 2.532 1.347 0 -0.879 -0.879 0 1.347 2.532


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



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