Results for Point Group S16



Symmetric powers of degenerate representation E3
Vibrational overtones


Characters of symmetric powers
Power
To
E S16 C8 (S16)3 C4 (S16)5 (C8)3 (S16)7 C2 (S16)9 (C8)5 (S16)11 (C4)3 (S16)13 (C8)7 (S16)15
1 2 0.765 -1.414 -1.848 0 1.848 1.414 -0.765 -2 -0.765 1.414 1.848 0 -1.848 -1.414 0.765
2 3 -0.414 1.000 2.414 -1 2.414 1.000 -0.414 3 -0.414 1.000 2.414 -1 2.414 1.000 -0.414
3 4 -1.082 0.000 -2.613 0 2.613 0.000 1.082 -4 1.082 -0.000 2.613 0 -2.613 -0.000 -1.082
4 5 -0.414 -1.000 2.414 1 2.414 -1.000 -0.414 5 -0.414 -1.000 2.414 1 2.414 -1.000 -0.414
5 6 0.765 1.414 -1.848 0 1.848 -1.414 -0.765 -6 -0.765 -1.414 1.848 0 -1.848 1.414 0.765
6 7 1.000 -1.000 1.000 -1 1.000 -1.000 1.000 7 1.000 -1.000 1.000 -1 1.000 -1.000 1.000
7 8 0.000 -0.000 -0.000 0 -0.000 -0.000 -0.000 -8 -0.000 0.000 0.000 0 0.000 0.000 -0.000
8 9 -1.000 1.000 -1.000 1 -1.000 1.000 -1.000 9 -1.000 1.000 -1.000 1 -1.000 1.000 -1.000
9 10 -0.765 -1.414 1.848 0 -1.848 1.414 0.765 -10 0.765 1.414 -1.848 0 1.848 -1.414 -0.765
10 11 0.414 1.000 -2.414 -1 -2.414 1.000 0.414 11 0.414 1.000 -2.414 -1 -2.414 1.000 0.414
11 12 1.082 0.000 2.613 0 -2.613 0.000 -1.082 -12 -1.082 -0.000 -2.613 0 2.613 -0.000 1.082
12 13 0.414 -1.000 -2.414 1 -2.414 -1.000 0.414 13 0.414 -1.000 -2.414 1 -2.414 -1.000 0.414
13 14 -0.765 1.414 1.848 0 -1.848 -1.414 0.765 -14 0.765 -1.414 -1.848 0 1.848 1.414 -0.765
14 15 -1.000 -1.000 -1.000 -1 -1.000 -1.000 -1.000 15 -1.000 -1.000 -1.000 -1 -1.000 -1.000 -1.000
15 16 -0.000 -0.000 0.000 0 0.000 -0.000 -0.000 -16 0.000 0.000 -0.000 0 -0.000 0.000 0.000
16 17 1.000 1.000 1.000 1 1.000 1.000 1.000 17 1.000 1.000 1.000 1 1.000 1.000 1.000
17 18 0.765 -1.414 -1.848 0 1.848 1.414 -0.765 -18 -0.765 1.414 1.848 0 -1.848 -1.414 0.765
18 19 -0.414 1.000 2.414 -1 2.414 1.000 -0.414 19 -0.414 1.000 2.414 -1 2.414 1.000 -0.414
19 20 -1.082 0.000 -2.613 0 2.613 0.000 1.082 -20 1.082 -0.000 2.613 0 -2.613 -0.000 -1.082
20 21 -0.414 -1.000 2.414 1 2.414 -1.000 -0.414 21 -0.414 -1.000 2.414 1 2.414 -1.000 -0.414


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



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