Results for Point Group D10d



Symmetric powers of degenerate representation E7
Vibrational overtones


Characters of symmetric powers
Power
To
E 2S20 2C10 2(S20)3 2C5 2S4 2(C10)3 2(S20)7 2(C5)2 2(S20)9 C2 10C'2 10σd
1 2 -1.176 -0.618 1.902 -1.618 0 1.618 -1.902 0.618 1.176 -2 0 0
2 3 0.382 -0.618 2.618 1.618 -1 1.618 2.618 -0.618 0.382 3 1 1
3 4 0.727 1.000 3.078 -1.000 0 1.000 -3.078 -1.000 -0.727 -4 0 0
4 5 -1.236 -0.000 3.236 -0.000 1 -0.000 3.236 0.000 -1.236 5 1 1
5 6 0.727 -1.000 3.078 1.000 0 -1.000 -3.078 1.000 -0.727 -6 0 0
6 7 0.382 0.618 2.618 -1.618 -1 -1.618 2.618 0.618 0.382 7 1 1
7 8 -1.176 0.618 1.902 1.618 0 -1.618 -1.902 -0.618 1.176 -8 0 0
8 9 1.000 -1.000 1.000 -1.000 1 -1.000 1.000 -1.000 1.000 9 1 1
9 10 0.000 0.000 -0.000 -0.000 0 0.000 0.000 0.000 -0.000 -10 0 0
10 11 -1.000 1.000 -1.000 1.000 -1 1.000 -1.000 1.000 -1.000 11 1 1
11 12 1.176 -0.618 -1.902 -1.618 0 1.618 1.902 0.618 -1.176 -12 0 0
12 13 -0.382 -0.618 -2.618 1.618 1 1.618 -2.618 -0.618 -0.382 13 1 1
13 14 -0.727 1.000 -3.078 -1.000 0 1.000 3.078 -1.000 0.727 -14 0 0
14 15 1.236 -0.000 -3.236 -0.000 -1 -0.000 -3.236 0.000 1.236 15 1 1
15 16 -0.727 -1.000 -3.078 1.000 0 -1.000 3.078 1.000 0.727 -16 0 0
16 17 -0.382 0.618 -2.618 -1.618 1 -1.618 -2.618 0.618 -0.382 17 1 1
17 18 1.176 0.618 -1.902 1.618 0 -1.618 1.902 -0.618 -1.176 -18 0 0
18 19 -1.000 -1.000 -1.000 -1.000 -1 -1.000 -1.000 -1.000 -1.000 19 1 1
19 20 -0.000 0.000 0.000 -0.000 0 0.000 -0.000 0.000 0.000 -20 0 0
20 21 1.000 1.000 1.000 1.000 1 1.000 1.000 1.000 1.000 21 1 1


Decomposition to irreducible representations
Power
To
A1 A2 B1 B2 E1 E2 E3 E4 E5 E6 E7 E8 E9
1 0 0 0 0 0 0 0 0 0 0 1 0 0 E7
2 1 0 0 0 0 0 0 0 0 1 0 0 0 A1⊕E6
3 0 0 0 0 1 0 0 0 0 0 1 0 0 E1⊕E7
4 1 0 0 0 0 0 0 0 0 1 0 1 0 A1⊕E6⊕E8
5 0 0 0 0 1 0 0 0 1 0 1 0 0 E1⊕E5⊕E7
6 1 0 0 0 0 1 0 0 0 1 0 1 0 A1⊕E2⊕E6⊕E8
7 0 0 0 0 1 0 0 0 1 0 1 0 1 E1⊕E5⊕E7⊕E9
8 1 0 0 0 0 1 0 1 0 1 0 1 0 A1⊕E2⊕E4⊕E6⊕E8
9 0 0 0 0 1 0 1 0 1 0 1 0 1 E1⊕E3⊕E5⊕E7⊕E9
10 1 0 1 1 0 1 0 1 0 1 0 1 0 A1⊕B1⊕B2⊕E2⊕E4⊕E6⊕E8
11 0 0 0 0 1 0 2 0 1 0 1 0 1 E1⊕2E3⊕E5⊕E7⊕E9
12 1 0 1 1 0 1 0 2 0 1 0 1 0 A1⊕B1⊕B2⊕E2⊕2E4⊕E6⊕E8
13 0 0 0 0 1 0 2 0 1 0 1 0 2 E1⊕2E3⊕E5⊕E7⊕2E9
14 1 0 1 1 0 2 0 2 0 1 0 1 0 A1⊕B1⊕B2⊕2E2⊕2E4⊕E6⊕E8
15 0 0 0 0 1 0 2 0 2 0 1 0 2 E1⊕2E3⊕2E5⊕E7⊕2E9
16 1 0 1 1 0 2 0 2 0 1 0 2 0 A1⊕B1⊕B2⊕2E2⊕2E4⊕E6⊕2E8
17 0 0 0 0 2 0 2 0 2 0 1 0 2 2E1⊕2E3⊕2E5⊕E7⊕2E9
18 1 0 1 1 0 2 0 2 0 2 0 2 0 A1⊕B1⊕B2⊕2E2⊕2E4⊕2E6⊕2E8
19 0 0 0 0 2 0 2 0 2 0 2 0 2 2E1⊕2E3⊕2E5⊕2E7⊕2E9
20 2 1 1 1 0 2 0 2 0 2 0 2 0 2A1⊕A2⊕B1⊕B2⊕2E2⊕2E4⊕2E6⊕2E8



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