Results for Point Group D15



Symmetric powers of degenerate representation E7
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 -1.956 1.827 -1.618 1.338 -1 0.618 -0.209 0
2 3 2.827 2.338 1.618 0.791 0 -0.618 -0.956 1
3 4 -3.574 2.445 -1.000 -0.280 1 -1.000 0.409 0
4 5 4.165 2.129 -0.000 -1.165 -1 0.000 0.871 1
5 6 -4.574 1.445 1.000 -1.280 0 1.000 -0.591 0
6 7 4.783 0.511 -1.618 -0.547 1 0.618 -0.747 1
7 8 -4.783 -0.511 1.618 0.547 -1 -0.618 0.747 0
8 9 4.574 -1.445 -1.000 1.280 0 -1.000 0.591 1
9 10 -4.165 -2.129 -0.000 1.165 1 0.000 -0.871 0
10 11 3.574 -2.445 1.000 0.280 -1 1.000 -0.409 1
11 12 -2.827 -2.338 -1.618 -0.791 0 0.618 0.956 0
12 13 1.956 -1.827 1.618 -1.338 1 -0.618 0.209 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 -1.956 1.827 -1.618 1.338 -1 0.618 -0.209 1
17 18 2.827 2.338 1.618 0.791 0 -0.618 -0.956 0
18 19 -3.574 2.445 -1.000 -0.280 1 -1.000 0.409 1
19 20 4.165 2.129 -0.000 -1.165 -1 0.000 0.871 0
20 21 -4.574 1.445 1.000 -1.280 0 1.000 -0.591 1


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


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