Results for Point Group C13



Symmetric powers of degenerate representation E6
Vibrational overtones


Characters of symmetric powers
Power
To
E C13 (C13)2 (C13)3 (C13)4 (C13)5 (C13)6 (C13)7 (C13)8 (C13)9 (C13)10 (C13)11 (C13)12
1 2 -1.942 1.771 -1.497 1.136 -0.709 0.241 0.241 -0.709 1.136 -1.497 1.771 -1.942
2 3 2.771 2.136 1.241 0.291 -0.497 -0.942 -0.942 -0.497 0.291 1.241 2.136 2.771
3 4 -3.439 2.012 -0.361 -0.806 1.062 -0.468 -0.468 1.062 -0.806 -0.361 2.012 -3.439
4 5 3.907 1.427 -0.701 -1.206 -0.256 0.829 0.829 -0.256 -1.206 -0.701 1.427 3.907
5 6 -4.148 0.515 1.410 -0.565 -0.880 0.668 0.668 -0.880 -0.565 1.410 0.515 -4.148
6 7 4.148 -0.515 -1.410 0.565 0.880 -0.668 -0.668 0.880 0.565 -1.410 -0.515 4.148
7 8 -3.907 -1.427 0.701 1.206 0.256 -0.829 -0.829 0.256 1.206 0.701 -1.427 -3.907
8 9 3.439 -2.012 0.361 0.806 -1.062 0.468 0.468 -1.062 0.806 0.361 -2.012 3.439
9 10 -2.771 -2.136 -1.241 -0.291 0.497 0.942 0.942 0.497 -0.291 -1.241 -2.136 -2.771
10 11 1.942 -1.771 1.497 -1.136 0.709 -0.241 -0.241 0.709 -1.136 1.497 -1.771 1.942
11 12 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000
12 13 -0.000 0.000 -0.000 0.000 -0.000 0.000 -0.000 0.000 -0.000 0.000 -0.000 0.000
13 14 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
14 15 -1.942 1.771 -1.497 1.136 -0.709 0.241 0.241 -0.709 1.136 -1.497 1.771 -1.942
15 16 2.771 2.136 1.241 0.291 -0.497 -0.942 -0.942 -0.497 0.291 1.241 2.136 2.771
16 17 -3.439 2.012 -0.361 -0.806 1.062 -0.468 -0.468 1.062 -0.806 -0.361 2.012 -3.439
17 18 3.907 1.427 -0.701 -1.206 -0.256 0.829 0.829 -0.256 -1.206 -0.701 1.427 3.907
18 19 -4.148 0.515 1.410 -0.565 -0.880 0.668 0.668 -0.880 -0.565 1.410 0.515 -4.148
19 20 4.148 -0.515 -1.410 0.565 0.880 -0.668 -0.668 0.880 0.565 -1.410 -0.515 4.148
20 21 -3.907 -1.427 0.701 1.206 0.256 -0.829 -0.829 0.256 1.206 0.701 -1.427 -3.907


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



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