Results for Point Group C19



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


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


Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement