Results for Point Group D19



Symmetric powers of degenerate representation E7
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 -1.355 -0.165 1.578 -1.973 1.094 0.491 -1.759 1.892 -0.803 0
2 3 0.835 -0.973 1.491 2.892 0.197 -0.759 2.094 2.578 -0.355 1
3 4 0.224 0.326 0.775 -3.732 -0.879 -0.864 -1.924 2.986 1.088 0
4 5 -1.138 0.919 -0.268 4.470 -1.158 0.335 1.291 3.069 -0.520 1
5 6 1.318 -0.478 -1.198 -5.086 -0.388 1.028 -0.346 2.820 -0.671 0
6 7 -0.647 -0.840 -1.623 5.564 0.734 0.170 -0.682 2.266 1.059 1
7 8 -0.441 0.616 -1.363 -5.890 1.190 -0.945 1.546 1.466 -0.180 0
8 9 1.245 0.738 -0.529 6.055 0.569 -0.634 -2.037 0.507 -0.914 1
9 10 -1.245 -0.738 0.529 -6.055 -0.569 0.634 2.037 -0.507 0.914 0
10 11 0.441 -0.616 1.363 5.890 -1.190 0.945 -1.546 -1.466 0.180 1
11 12 0.647 0.840 1.623 -5.564 -0.734 -0.170 0.682 -2.266 -1.059 0
12 13 -1.318 0.478 1.198 5.086 0.388 -1.028 0.346 -2.820 0.671 1
13 14 1.138 -0.919 0.268 -4.470 1.158 -0.335 -1.291 -3.069 0.520 0
14 15 -0.224 -0.326 -0.775 3.732 0.879 0.864 1.924 -2.986 -1.088 1
15 16 -0.835 0.973 -1.491 -2.892 -0.197 0.759 -2.094 -2.578 0.355 0
16 17 1.355 0.165 -1.578 1.973 -1.094 -0.491 1.759 -1.892 0.803 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 -1.355 -0.165 1.578 -1.973 1.094 0.491 -1.759 1.892 -0.803 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 1 0 0 E7
2 1 0 0 0 0 0 1 0 0 0 0 A1⊕E5
3 0 0 0 1 0 0 0 0 1 0 0 E2⊕E7
4 1 0 0 0 0 0 1 0 0 0 1 A1⊕E5⊕E9
5 0 0 0 1 1 0 0 0 1 0 0 E2⊕E3⊕E7
6 1 0 0 0 0 1 1 0 0 0 1 A1⊕E4⊕E5⊕E9
7 0 0 0 1 1 0 0 0 1 1 0 E2⊕E3⊕E7⊕E8
8 1 0 1 0 0 1 1 0 0 0 1 A1⊕E1⊕E4⊕E5⊕E9
9 0 0 0 1 1 0 0 1 1 1 0 E2⊕E3⊕E6⊕E7⊕E8
10 1 0 1 0 0 1 1 1 0 0 1 A1⊕E1⊕E4⊕E5⊕E6⊕E9
11 0 0 1 1 1 0 0 1 1 1 0 E1⊕E2⊕E3⊕E6⊕E7⊕E8
12 1 0 1 0 0 1 1 1 0 1 1 A1⊕E1⊕E4⊕E5⊕E6⊕E8⊕E9
13 0 0 1 1 1 1 0 1 1 1 0 E1⊕E2⊕E3⊕E4⊕E6⊕E7⊕E8
14 1 0 1 0 1 1 1 1 0 1 1 A1⊕E1⊕E3⊕E4⊕E5⊕E6⊕E8⊕E9
15 0 0 1 1 1 1 0 1 1 1 1 E1⊕E2⊕E3⊕E4⊕E6⊕E7⊕E8⊕E9
16 1 0 1 1 1 1 1 1 0 1 1 A1⊕E1⊕E2⊕E3⊕E4⊕E5⊕E6⊕E8⊕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 2 1 1 A1⊕E1⊕E2⊕E3⊕E4⊕E5⊕E6⊕2E7⊕E8⊕E9



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