Results for Point Group C9



Symmetric powers of degenerate representation E4
Vibrational overtones


Characters of symmetric powers
Power
To		 E C9 (C9)2 C3 (C9)4 (C9)5 (C3)2 (C9)7 (C9)8
1 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 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 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 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 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 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 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 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 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 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


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


Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement