Results for Point Group C19v



Symmetric powers of degenerate representation E9
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 19σv
1 2 -1.973 1.892 -1.759 1.578 -1.355 1.094 -0.803 0.491 -0.165 0
2 3 2.892 2.578 2.094 1.491 0.835 0.197 -0.355 -0.759 -0.973 1
3 4 -3.732 2.986 -1.924 0.775 0.224 -0.879 1.088 -0.864 0.326 0
4 5 4.470 3.069 1.291 -0.268 -1.138 -1.158 -0.520 0.335 0.919 1
5 6 -5.086 2.820 -0.346 -1.198 1.318 -0.388 -0.671 1.028 -0.478 0
6 7 5.564 2.266 -0.682 -1.623 -0.647 0.734 1.059 0.170 -0.840 1
7 8 -5.890 1.466 1.546 -1.363 -0.441 1.190 -0.180 -0.945 0.616 0
8 9 6.055 0.507 -2.037 -0.529 1.245 0.569 -0.914 -0.634 0.738 1
9 10 -6.055 -0.507 2.037 0.529 -1.245 -0.569 0.914 0.634 -0.738 0
10 11 5.890 -1.466 -1.546 1.363 0.441 -1.190 0.180 0.945 -0.616 1
11 12 -5.564 -2.266 0.682 1.623 0.647 -0.734 -1.059 -0.170 0.840 0
12 13 5.086 -2.820 0.346 1.198 -1.318 0.388 0.671 -1.028 0.478 1
13 14 -4.470 -3.069 -1.291 0.268 1.138 1.158 0.520 -0.335 -0.919 0
14 15 3.732 -2.986 1.924 -0.775 -0.224 0.879 -1.088 0.864 -0.326 1
15 16 -2.892 -2.578 -2.094 -1.491 -0.835 -0.197 0.355 0.759 0.973 0
16 17 1.973 -1.892 1.759 -1.578 1.355 -1.094 0.803 -0.491 0.165 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 -1.973 1.892 -1.759 1.578 -1.355 1.094 -0.803 0.491 -0.165 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 0 1 E9
2 1 0 1 0 0 0 0 0 0 0 0 A1⊕E1
3 0 0 0 0 0 0 0 0 0 1 1 E8⊕E9
4 1 0 1 1 0 0 0 0 0 0 0 A1⊕E1⊕E2
5 0 0 0 0 0 0 0 0 1 1 1 E7⊕E8⊕E9
6 1 0 1 1 1 0 0 0 0 0 0 A1⊕E1⊕E2⊕E3
7 0 0 0 0 0 0 0 1 1 1 1 E6⊕E7⊕E8⊕E9
8 1 0 1 1 1 1 0 0 0 0 0 A1⊕E1⊕E2⊕E3⊕E4
9 0 0 0 0 0 0 1 1 1 1 1 E5⊕E6⊕E7⊕E8⊕E9
10 1 0 1 1 1 1 1 0 0 0 0 A1⊕E1⊕E2⊕E3⊕E4⊕E5
11 0 0 0 0 0 1 1 1 1 1 1 E4⊕E5⊕E6⊕E7⊕E8⊕E9
12 1 0 1 1 1 1 1 1 0 0 0 A1⊕E1⊕E2⊕E3⊕E4⊕E5⊕E6
13 0 0 0 0 1 1 1 1 1 1 1 E3⊕E4⊕E5⊕E6⊕E7⊕E8⊕E9
14 1 0 1 1 1 1 1 1 1 0 0 A1⊕E1⊕E2⊕E3⊕E4⊕E5⊕E6⊕E7
15 0 0 0 1 1 1 1 1 1 1 1 E2⊕E3⊕E4⊕E5⊕E6⊕E7⊕E8⊕E9
16 1 0 1 1 1 1 1 1 1 1 0 A1⊕E1⊕E2⊕E3⊕E4⊕E5⊕E6⊕E7⊕E8
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 1 2 A1⊕E1⊕E2⊕E3⊕E4⊕E5⊕E6⊕E7⊕E8⊕2E9



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