Results for Point Group D10d



Symmetric powers of degenerate representation E6
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 -0.618 -1.618 1.618 0.618 -2 0.618 1.618 -1.618 -0.618 2 0 0
2 3 -0.618 1.618 1.618 -0.618 3 -0.618 1.618 1.618 -0.618 3 1 1
3 4 1.000 -1.000 1.000 -1.000 -4 -1.000 1.000 -1.000 1.000 4 0 0
4 5 0.000 0.000 -0.000 -0.000 5 0.000 0.000 -0.000 -0.000 5 1 1
5 6 -1.000 1.000 -1.000 1.000 -6 1.000 -1.000 1.000 -1.000 6 0 0
6 7 0.618 -1.618 -1.618 0.618 7 0.618 -1.618 -1.618 0.618 7 1 1
7 8 0.618 1.618 -1.618 -0.618 -8 -0.618 -1.618 1.618 0.618 8 0 0
8 9 -1.000 -1.000 -1.000 -1.000 9 -1.000 -1.000 -1.000 -1.000 9 1 1
9 10 -0.000 0.000 0.000 -0.000 -10 0.000 -0.000 -0.000 0.000 10 0 0
10 11 1.000 1.000 1.000 1.000 11 1.000 1.000 1.000 1.000 11 1 1
11 12 -0.618 -1.618 1.618 0.618 -12 0.618 1.618 -1.618 -0.618 12 0 0
12 13 -0.618 1.618 1.618 -0.618 13 -0.618 1.618 1.618 -0.618 13 1 1
13 14 1.000 -1.000 1.000 -1.000 -14 -1.000 1.000 -1.000 1.000 14 0 0
14 15 0.000 0.000 -0.000 -0.000 15 0.000 0.000 -0.000 -0.000 15 1 1
15 16 -1.000 1.000 -1.000 1.000 -16 1.000 -1.000 1.000 -1.000 16 0 0
16 17 0.618 -1.618 -1.618 0.618 17 0.618 -1.618 -1.618 0.618 17 1 1
17 18 0.618 1.618 -1.618 -0.618 -18 -0.618 -1.618 1.618 0.618 18 0 0
18 19 -1.000 -1.000 -1.000 -1.000 19 -1.000 -1.000 -1.000 -1.000 19 1 1
19 20 -0.000 0.000 0.000 -0.000 -20 0.000 -0.000 -0.000 0.000 20 0 0
20 21 1.000 1.000 1.000 1.000 21 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 1 0 0 0 E6
2 1 0 0 0 0 0 0 0 0 0 0 1 0 A1⊕E8
3 0 0 0 0 0 1 0 0 0 1 0 0 0 E2⊕E6
4 1 0 0 0 0 0 0 1 0 0 0 1 0 A1⊕E4⊕E8
5 0 0 1 1 0 1 0 0 0 1 0 0 0 B1⊕B2⊕E2⊕E6
6 1 0 0 0 0 0 0 2 0 0 0 1 0 A1⊕2E4⊕E8
7 0 0 1 1 0 2 0 0 0 1 0 0 0 B1⊕B2⊕2E2⊕E6
8 1 0 0 0 0 0 0 2 0 0 0 2 0 A1⊕2E4⊕2E8
9 0 0 1 1 0 2 0 0 0 2 0 0 0 B1⊕B2⊕2E2⊕2E6
10 2 1 0 0 0 0 0 2 0 0 0 2 0 2A1⊕A2⊕2E4⊕2E8
11 0 0 1 1 0 2 0 0 0 3 0 0 0 B1⊕B2⊕2E2⊕3E6
12 2 1 0 0 0 0 0 2 0 0 0 3 0 2A1⊕A2⊕2E4⊕3E8
13 0 0 1 1 0 3 0 0 0 3 0 0 0 B1⊕B2⊕3E2⊕3E6
14 2 1 0 0 0 0 0 3 0 0 0 3 0 2A1⊕A2⊕3E4⊕3E8
15 0 0 2 2 0 3 0 0 0 3 0 0 0 2B1⊕2B2⊕3E2⊕3E6
16 2 1 0 0 0 0 0 4 0 0 0 3 0 2A1⊕A2⊕4E4⊕3E8
17 0 0 2 2 0 4 0 0 0 3 0 0 0 2B1⊕2B2⊕4E2⊕3E6
18 2 1 0 0 0 0 0 4 0 0 0 4 0 2A1⊕A2⊕4E4⊕4E8
19 0 0 2 2 0 4 0 0 0 4 0 0 0 2B1⊕2B2⊕4E2⊕4E6
20 3 2 0 0 0 0 0 4 0 0 0 4 0 3A1⊕2A2⊕4E4⊕4E8


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