Results for Point Group D15



Symmetric powers of degenerate representation E4
Vibrational overtones


Characters of symmetric powers
Power
To
E 2C15 2(C15)2 2C5 2(C15)4 2C3 2(C5)2 2(C15)7 15C'2
1 2 -0.209 -1.956 0.618 1.827 -1 -1.618 1.338 0
2 3 -0.956 2.827 -0.618 2.338 0 1.618 0.791 1
3 4 0.409 -3.574 -1.000 2.445 1 -1.000 -0.280 0
4 5 0.871 4.165 0.000 2.129 -1 0.000 -1.165 1
5 6 -0.591 -4.574 1.000 1.445 0 1.000 -1.280 0
6 7 -0.747 4.783 0.618 0.511 1 -1.618 -0.547 1
7 8 0.747 -4.783 -0.618 -0.511 -1 1.618 0.547 0
8 9 0.591 4.574 -1.000 -1.445 0 -1.000 1.280 1
9 10 -0.871 -4.165 0.000 -2.129 1 0.000 1.165 0
10 11 -0.409 3.574 1.000 -2.445 -1 1.000 0.280 1
11 12 0.956 -2.827 0.618 -2.338 0 -1.618 -0.791 0
12 13 0.209 1.956 -0.618 -1.827 1 1.618 -1.338 1
13 14 -1.000 -1.000 -1.000 -1.000 -1 -1.000 -1.000 0
14 15 -0.000 0.000 0.000 -0.000 0 0.000 -0.000 1
15 16 1.000 1.000 1.000 1.000 1 1.000 1.000 0
16 17 -0.209 -1.956 0.618 1.827 -1 -1.618 1.338 1
17 18 -0.956 2.827 -0.618 2.338 0 1.618 0.791 0
18 19 0.409 -3.574 -1.000 2.445 1 -1.000 -0.280 1
19 20 0.871 4.165 0.000 2.129 -1 0.000 -1.165 0
20 21 -0.591 -4.574 1.000 1.445 0 1.000 -1.280 1


Decomposition to irreducible representations
Power
To
A1 A2 E1 E2 E3 E4 E5 E6 E7
1 0 0 0 0 0 1 0 0 0 E4
2 1 0 0 0 0 0 0 0 1 A1⊕E7
3 0 0 0 0 1 1 0 0 0 E3⊕E4
4 1 0 1 0 0 0 0 0 1 A1⊕E1⊕E7
5 0 0 0 0 1 1 1 0 0 E3⊕E4⊕E5
6 1 0 1 0 0 0 0 1 1 A1⊕E1⊕E6⊕E7
7 0 0 0 1 1 1 1 0 0 E2⊕E3⊕E4⊕E5
8 1 0 1 1 0 0 0 1 1 A1⊕E1⊕E2⊕E6⊕E7
9 0 0 0 1 1 1 1 1 0 E2⊕E3⊕E4⊕E5⊕E6
10 1 0 1 1 0 0 1 1 1 A1⊕E1⊕E2⊕E5⊕E6⊕E7
11 0 0 1 1 1 1 1 1 0 E1⊕E2⊕E3⊕E4⊕E5⊕E6
12 1 0 1 1 1 0 1 1 1 A1⊕E1⊕E2⊕E3⊕E5⊕E6⊕E7
13 0 0 1 1 1 1 1 1 1 E1⊕E2⊕E3⊕E4⊕E5⊕E6⊕E7
14 1 0 1 1 1 1 1 1 1 A1⊕E1⊕E2⊕E3⊕E4⊕E5⊕E6⊕E7
15 1 1 1 1 1 1 1 1 1 A1⊕A2⊕E1⊕E2⊕E3⊕E4⊕E5⊕E6⊕E7
16 1 0 1 1 1 2 1 1 1 A1⊕E1⊕E2⊕E3⊕2E4⊕E5⊕E6⊕E7
17 1 1 1 1 1 1 1 1 2 A1⊕A2⊕E1⊕E2⊕E3⊕E4⊕E5⊕E6⊕2E7
18 1 0 1 1 2 2 1 1 1 A1⊕E1⊕E2⊕2E3⊕2E4⊕E5⊕E6⊕E7
19 1 1 2 1 1 1 1 1 2 A1⊕A2⊕2E1⊕E2⊕E3⊕E4⊕E5⊕E6⊕2E7
20 1 0 1 1 2 2 2 1 1 A1⊕E1⊕E2⊕2E3⊕2E4⊕2E5⊕E6⊕E7



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