Results for Point Group D13



Symmetric powers of degenerate representation E6
Vibrational overtones


Characters of symmetric powers
Power
To		 E 2C13 2(C13)2 2(C13)3 2(C13)4 2(C13)5 2(C13)6 13C'2
1 2 -1.942 1.771 -1.497 1.136 -0.709 0.241 0
2 3 2.771 2.136 1.241 0.291 -0.497 -0.942 1
3 4 -3.439 2.012 -0.361 -0.806 1.062 -0.468 0
4 5 3.907 1.427 -0.701 -1.206 -0.256 0.829 1
5 6 -4.148 0.515 1.410 -0.565 -0.880 0.668 0
6 7 4.148 -0.515 -1.410 0.565 0.880 -0.668 1
7 8 -3.907 -1.427 0.701 1.206 0.256 -0.829 0
8 9 3.439 -2.012 0.361 0.806 -1.062 0.468 1
9 10 -2.771 -2.136 -1.241 -0.291 0.497 0.942 0
10 11 1.942 -1.771 1.497 -1.136 0.709 -0.241 1
11 12 -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 0
12 13 -0.000 -0.000 -0.000 -0.000 -0.000 0.000 1
13 14 1.000 1.000 1.000 1.000 1.000 1.000 0
14 15 -1.942 1.771 -1.497 1.136 -0.709 0.241 1
15 16 2.771 2.136 1.241 0.291 -0.497 -0.942 0
16 17 -3.439 2.012 -0.361 -0.806 1.062 -0.468 1
17 18 3.907 1.427 -0.701 -1.206 -0.256 0.829 0
18 19 -4.148 0.515 1.410 -0.565 -0.880 0.668 1
19 20 4.148 -0.515 -1.410 0.565 0.880 -0.668 0
20 21 -3.907 -1.427 0.701 1.206 0.256 -0.829 1


Decomposition to irreducible representations
Power
To		 A1 A2 E1 E2 E3 E4 E5 E6
1 0 0 0 0 0 0 0 1 E6
2 1 0 1 0 0 0 0 0 A1⊕E1
3 0 0 0 0 0 0 1 1 E5⊕E6
4 1 0 1 1 0 0 0 0 A1⊕E1⊕E2
5 0 0 0 0 0 1 1 1 E4⊕E5⊕E6
6 1 0 1 1 1 0 0 0 A1⊕E1⊕E2⊕E3
7 0 0 0 0 1 1 1 1 E3⊕E4⊕E5⊕E6
8 1 0 1 1 1 1 0 0 A1⊕E1⊕E2⊕E3⊕E4
9 0 0 0 1 1 1 1 1 E2⊕E3⊕E4⊕E5⊕E6
10 1 0 1 1 1 1 1 0 A1⊕E1⊕E2⊕E3⊕E4⊕E5
11 0 0 1 1 1 1 1 1 E1⊕E2⊕E3⊕E4⊕E5⊕E6
12 1 0 1 1 1 1 1 1 A1⊕E1⊕E2⊕E3⊕E4⊕E5⊕E6
13 1 1 1 1 1 1 1 1 A1⊕A2⊕E1⊕E2⊕E3⊕E4⊕E5⊕E6
14 1 0 1 1 1 1 1 2 A1⊕E1⊕E2⊕E3⊕E4⊕E5⊕2E6
15 1 1 2 1 1 1 1 1 A1⊕A2⊕2E1⊕E2⊕E3⊕E4⊕E5⊕E6
16 1 0 1 1 1 1 2 2 A1⊕E1⊕E2⊕E3⊕E4⊕2E5⊕2E6
17 1 1 2 2 1 1 1 1 A1⊕A2⊕2E1⊕2E2⊕E3⊕E4⊕E5⊕E6
18 1 0 1 1 1 2 2 2 A1⊕E1⊕E2⊕E3⊕2E4⊕2E5⊕2E6
19 1 1 2 2 2 1 1 1 A1⊕A2⊕2E1⊕2E2⊕2E3⊕E4⊕E5⊕E6
20 1 0 1 1 2 2 2 2 A1⊕E1⊕E2⊕2E3⊕2E4⊕2E5⊕2E6


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