Results for Point Group C19



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


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


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