Results for Point Group C13



Symmetric powers of degenerate representation E5
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 -1.497 0.241 1.136 -1.942 1.771 -0.709 -0.709 1.771 -1.942 1.136 0.241 -1.497
2 3 1.241 -0.942 0.291 2.771 2.136 -0.497 -0.497 2.136 2.771 0.291 -0.942 1.241
3 4 -0.361 -0.468 -0.806 -3.439 2.012 1.062 1.062 2.012 -3.439 -0.806 -0.468 -0.361
4 5 -0.701 0.829 -1.206 3.907 1.427 -0.256 -0.256 1.427 3.907 -1.206 0.829 -0.701
5 6 1.410 0.668 -0.565 -4.148 0.515 -0.880 -0.880 0.515 -4.148 -0.565 0.668 1.410
6 7 -1.410 -0.668 0.565 4.148 -0.515 0.880 0.880 -0.515 4.148 0.565 -0.668 -1.410
7 8 0.701 -0.829 1.206 -3.907 -1.427 0.256 0.256 -1.427 -3.907 1.206 -0.829 0.701
8 9 0.361 0.468 0.806 3.439 -2.012 -1.062 -1.062 -2.012 3.439 0.806 0.468 0.361
9 10 -1.241 0.942 -0.291 -2.771 -2.136 0.497 0.497 -2.136 -2.771 -0.291 0.942 -1.241
10 11 1.497 -0.241 -1.136 1.942 -1.771 0.709 0.709 -1.771 1.942 -1.136 -0.241 1.497
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 -1.497 0.241 1.136 -1.942 1.771 -0.709 -0.709 1.771 -1.942 1.136 0.241 -1.497
15 16 1.241 -0.942 0.291 2.771 2.136 -0.497 -0.497 2.136 2.771 0.291 -0.942 1.241
16 17 -0.361 -0.468 -0.806 -3.439 2.012 1.062 1.062 2.012 -3.439 -0.806 -0.468 -0.361
17 18 -0.701 0.829 -1.206 3.907 1.427 -0.256 -0.256 1.427 3.907 -1.206 0.829 -0.701
18 19 1.410 0.668 -0.565 -4.148 0.515 -0.880 -0.880 0.515 -4.148 -0.565 0.668 1.410
19 20 -1.410 -0.668 0.565 4.148 -0.515 0.880 0.880 -0.515 4.148 0.565 -0.668 -1.410
20 21 0.701 -0.829 1.206 -3.907 -1.427 0.256 0.256 -1.427 -3.907 1.206 -0.829 0.701


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


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