Results for Point Group D19



Symmetric powers of degenerate representation E8
Vibrational overtones


Characters of symmetric powers
Power
To
E 2C19 2(C19)2 2(C19)3 2(C19)4 2(C19)5 2(C19)6 2(C19)7 2(C19)8 2(C19)9 19C'2
1 2 -1.759 1.094 -0.165 -0.803 1.578 -1.973 1.892 -1.355 0.491 0
2 3 2.094 0.197 -0.973 -0.355 1.491 2.892 2.578 0.835 -0.759 1
3 4 -1.924 -0.879 0.326 1.088 0.775 -3.732 2.986 0.224 -0.864 0
4 5 1.291 -1.158 0.919 -0.520 -0.268 4.470 3.069 -1.138 0.335 1
5 6 -0.346 -0.388 -0.478 -0.671 -1.198 -5.086 2.820 1.318 1.028 0
6 7 -0.682 0.734 -0.840 1.059 -1.623 5.564 2.266 -0.647 0.170 1
7 8 1.546 1.190 0.616 -0.180 -1.363 -5.890 1.466 -0.441 -0.945 0
8 9 -2.037 0.569 0.738 -0.914 -0.529 6.055 0.507 1.245 -0.634 1
9 10 2.037 -0.569 -0.738 0.914 0.529 -6.055 -0.507 -1.245 0.634 0
10 11 -1.546 -1.190 -0.616 0.180 1.363 5.890 -1.466 0.441 0.945 1
11 12 0.682 -0.734 0.840 -1.059 1.623 -5.564 -2.266 0.647 -0.170 0
12 13 0.346 0.388 0.478 0.671 1.198 5.086 -2.820 -1.318 -1.028 1
13 14 -1.291 1.158 -0.919 0.520 0.268 -4.470 -3.069 1.138 -0.335 0
14 15 1.924 0.879 -0.326 -1.088 -0.775 3.732 -2.986 -0.224 0.864 1
15 16 -2.094 -0.197 0.973 0.355 -1.491 -2.892 -2.578 -0.835 0.759 0
16 17 1.759 -1.094 0.165 0.803 -1.578 1.973 -1.892 1.355 -0.491 1
17 18 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 0
18 19 -0.000 0.000 -0.000 0.000 0.000 -0.000 0.000 -0.000 0.000 1
19 20 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0
20 21 -1.759 1.094 -0.165 -0.803 1.578 -1.973 1.892 -1.355 0.491 1


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



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