Results for Point Group D12d



Symmetric powers of degenerate representation E9
Vibrational overtones


Characters of symmetric powers
Power
To		 E 2S24 2C12 2S8 2C6 2(S24)5 2C4 2(S24)7 2C3 2(S8)3 2(C12)5 2(S24)11 C2 12C'2 12σd
1 2 -1.414 0.000 1.414 -2 1.414 0 -1.414 2 -1.414 0.000 1.414 -2 0 0
2 3 1.000 -1.000 1.000 3 1.000 -1 1.000 3 1.000 -1.000 1.000 3 1 1
3 4 0.000 0.000 0.000 -4 0.000 0 0.000 4 0.000 0.000 0.000 -4 0 0
4 5 -1.000 1.000 -1.000 5 -1.000 1 -1.000 5 -1.000 1.000 -1.000 5 1 1
5 6 1.414 0.000 -1.414 -6 -1.414 0 1.414 6 1.414 0.000 -1.414 -6 0 0
6 7 -1.000 -1.000 -1.000 7 -1.000 -1 -1.000 7 -1.000 -1.000 -1.000 7 1 1
7 8 -0.000 0.000 -0.000 -8 -0.000 0 -0.000 8 -0.000 0.000 -0.000 -8 0 0
8 9 1.000 1.000 1.000 9 1.000 1 1.000 9 1.000 1.000 1.000 9 1 1
9 10 -1.414 0.000 1.414 -10 1.414 0 -1.414 10 -1.414 0.000 1.414 -10 0 0
10 11 1.000 -1.000 1.000 11 1.000 -1 1.000 11 1.000 -1.000 1.000 11 1 1
11 12 0.000 0.000 0.000 -12 0.000 0 0.000 12 0.000 0.000 0.000 -12 0 0
12 13 -1.000 1.000 -1.000 13 -1.000 1 -1.000 13 -1.000 1.000 -1.000 13 1 1
13 14 1.414 0.000 -1.414 -14 -1.414 0 1.414 14 1.414 0.000 -1.414 -14 0 0
14 15 -1.000 -1.000 -1.000 15 -1.000 -1 -1.000 15 -1.000 -1.000 -1.000 15 1 1
15 16 -0.000 0.000 -0.000 -16 -0.000 0 -0.000 16 -0.000 0.000 -0.000 -16 0 0
16 17 1.000 1.000 1.000 17 1.000 1 1.000 17 1.000 1.000 1.000 17 1 1
17 18 -1.414 0.000 1.414 -18 1.414 0 -1.414 18 -1.414 0.000 1.414 -18 0 0
18 19 1.000 -1.000 1.000 19 1.000 -1 1.000 19 1.000 -1.000 1.000 19 1 1
19 20 0.000 0.000 0.000 -20 0.000 0 0.000 20 0.000 0.000 0.000 -20 0 0
20 21 -1.000 1.000 -1.000 21 -1.000 1 -1.000 21 -1.000 1.000 -1.000 21 1 1


Decomposition to irreducible representations
Power
To		 A1 A2 B1 B2 E1 E2 E3 E4 E5 E6 E7 E8 E9 E10 E11
1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 E9
2 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 A1⊕E6
3 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 E3⊕E9
4 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 A1⊕B1⊕B2⊕E6
5 0 0 0 0 0 0 2 0 0 0 0 0 1 0 0 2E3⊕E9
6 1 0 1 1 0 0 0 0 0 2 0 0 0 0 0 A1⊕B1⊕B2⊕2E6
7 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 2E3⊕2E9
8 2 1 1 1 0 0 0 0 0 2 0 0 0 0 0 2A1⊕A2⊕B1⊕B2⊕2E6
9 0 0 0 0 0 0 2 0 0 0 0 0 3 0 0 2E3⊕3E9
10 2 1 1 1 0 0 0 0 0 3 0 0 0 0 0 2A1⊕A2⊕B1⊕B2⊕3E6
11 0 0 0 0 0 0 3 0 0 0 0 0 3 0 0 3E3⊕3E9
12 2 1 2 2 0 0 0 0 0 3 0 0 0 0 0 2A1⊕A2⊕2B1⊕2B2⊕3E6
13 0 0 0 0 0 0 4 0 0 0 0 0 3 0 0 4E3⊕3E9
14 2 1 2 2 0 0 0 0 0 4 0 0 0 0 0 2A1⊕A2⊕2B1⊕2B2⊕4E6
15 0 0 0 0 0 0 4 0 0 0 0 0 4 0 0 4E3⊕4E9
16 3 2 2 2 0 0 0 0 0 4 0 0 0 0 0 3A1⊕2A2⊕2B1⊕2B2⊕4E6
17 0 0 0 0 0 0 4 0 0 0 0 0 5 0 0 4E3⊕5E9
18 3 2 2 2 0 0 0 0 0 5 0 0 0 0 0 3A1⊕2A2⊕2B1⊕2B2⊕5E6
19 0 0 0 0 0 0 5 0 0 0 0 0 5 0 0 5E3⊕5E9
20 3 2 3 3 0 0 0 0 0 5 0 0 0 0 0 3A1⊕2A2⊕3B1⊕3B2⊕5E6


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