Results for Point Group C19



Symmetric powers of degenerate representation E8
Vibrational overtones


Characters of symmetric powers
Power
To
E C19 (C19)2 (C19)3 (C19)4 (C19)5 (C19)6 (C19)7 (C19)8 (C19)9 (C19)10 (C19)11 (C19)12 (C19)13 (C19)14 (C19)15 (C19)16 (C19)17 (C19)18
1 2 -1.759 1.094 -0.165 -0.803 1.578 -1.973 1.892 -1.355 0.491 0.491 -1.355 1.892 -1.973 1.578 -0.803 -0.165 1.094 -1.759
2 3 2.094 0.197 -0.973 -0.355 1.491 2.892 2.578 0.835 -0.759 -0.759 0.835 2.578 2.892 1.491 -0.355 -0.973 0.197 2.094
3 4 -1.924 -0.879 0.326 1.088 0.775 -3.732 2.986 0.224 -0.864 -0.864 0.224 2.986 -3.732 0.775 1.088 0.326 -0.879 -1.924
4 5 1.291 -1.158 0.919 -0.520 -0.268 4.470 3.069 -1.138 0.335 0.335 -1.138 3.069 4.470 -0.268 -0.520 0.919 -1.158 1.291
5 6 -0.346 -0.388 -0.478 -0.671 -1.198 -5.086 2.820 1.318 1.028 1.028 1.318 2.820 -5.086 -1.198 -0.671 -0.478 -0.388 -0.346
6 7 -0.682 0.734 -0.840 1.059 -1.623 5.564 2.266 -0.647 0.170 0.170 -0.647 2.266 5.564 -1.623 1.059 -0.840 0.734 -0.682
7 8 1.546 1.190 0.616 -0.180 -1.363 -5.890 1.466 -0.441 -0.945 -0.945 -0.441 1.466 -5.890 -1.363 -0.180 0.616 1.190 1.546
8 9 -2.037 0.569 0.738 -0.914 -0.529 6.055 0.507 1.245 -0.634 -0.634 1.245 0.507 6.055 -0.529 -0.914 0.738 0.569 -2.037
9 10 2.037 -0.569 -0.738 0.914 0.529 -6.055 -0.507 -1.245 0.634 0.634 -1.245 -0.507 -6.055 0.529 0.914 -0.738 -0.569 2.037
10 11 -1.546 -1.190 -0.616 0.180 1.363 5.890 -1.466 0.441 0.945 0.945 0.441 -1.466 5.890 1.363 0.180 -0.616 -1.190 -1.546
11 12 0.682 -0.734 0.840 -1.059 1.623 -5.564 -2.266 0.647 -0.170 -0.170 0.647 -2.266 -5.564 1.623 -1.059 0.840 -0.734 0.682
12 13 0.346 0.388 0.478 0.671 1.198 5.086 -2.820 -1.318 -1.028 -1.028 -1.318 -2.820 5.086 1.198 0.671 0.478 0.388 0.346
13 14 -1.291 1.158 -0.919 0.520 0.268 -4.470 -3.069 1.138 -0.335 -0.335 1.138 -3.069 -4.470 0.268 0.520 -0.919 1.158 -1.291
14 15 1.924 0.879 -0.326 -1.088 -0.775 3.732 -2.986 -0.224 0.864 0.864 -0.224 -2.986 3.732 -0.775 -1.088 -0.326 0.879 1.924
15 16 -2.094 -0.197 0.973 0.355 -1.491 -2.892 -2.578 -0.835 0.759 0.759 -0.835 -2.578 -2.892 -1.491 0.355 0.973 -0.197 -2.094
16 17 1.759 -1.094 0.165 0.803 -1.578 1.973 -1.892 1.355 -0.491 -0.491 1.355 -1.892 1.973 -1.578 0.803 0.165 -1.094 1.759
17 18 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000
18 19 -0.000 0.000 -0.000 0.000 -0.000 0.000 0.000 -0.000 0.000 -0.000 0.000 -0.000 -0.000 0.000 -0.000 0.000 0.000 0.000
19 20 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
20 21 -1.759 1.094 -0.165 -0.803 1.578 -1.973 1.892 -1.355 0.491 0.491 -1.355 1.892 -1.973 1.578 -0.803 -0.165 1.094 -1.759


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



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