Results for Point Group S10



Symmetric powers of degenerate representation E2u
Vibrational overtones


Characters of symmetric powers
Power
To		 E C5 (C5)2 (C5)3 (C5)4 i (S10)7 (S10)9 S10 (S10)3
1 2 -1.618 0.618 0.618 -1.618 -2 1.618 -0.618 -0.618 1.618
2 3 1.618 -0.618 -0.618 1.618 3 1.618 -0.618 -0.618 1.618
3 4 -1.000 -1.000 -1.000 -1.000 -4 1.000 1.000 1.000 1.000
4 5 -0.000 0.000 -0.000 0.000 5 -0.000 0.000 -0.000 0.000
5 6 1.000 1.000 1.000 1.000 -6 -1.000 -1.000 -1.000 -1.000
6 7 -1.618 0.618 0.618 -1.618 7 -1.618 0.618 0.618 -1.618
7 8 1.618 -0.618 -0.618 1.618 -8 -1.618 0.618 0.618 -1.618
8 9 -1.000 -1.000 -1.000 -1.000 9 -1.000 -1.000 -1.000 -1.000
9 10 -0.000 0.000 -0.000 0.000 -10 0.000 -0.000 0.000 -0.000
10 11 1.000 1.000 1.000 1.000 11 1.000 1.000 1.000 1.000
11 12 -1.618 0.618 0.618 -1.618 -12 1.618 -0.618 -0.618 1.618
12 13 1.618 -0.618 -0.618 1.618 13 1.618 -0.618 -0.618 1.618
13 14 -1.000 -1.000 -1.000 -1.000 -14 1.000 1.000 1.000 1.000
14 15 -0.000 0.000 -0.000 0.000 15 -0.000 0.000 -0.000 0.000
15 16 1.000 1.000 1.000 1.000 -16 -1.000 -1.000 -1.000 -1.000
16 17 -1.618 0.618 0.618 -1.618 17 -1.618 0.618 0.618 -1.618
17 18 1.618 -0.618 -0.618 1.618 -18 -1.618 0.618 0.618 -1.618
18 19 -1.000 -1.000 -1.000 -1.000 19 -1.000 -1.000 -1.000 -1.000
19 20 -0.000 0.000 -0.000 0.000 -20 0.000 -0.000 0.000 -0.000
20 21 1.000 1.000 1.000 1.000 21 1.000 1.000 1.000 1.000


Decomposition to irreducible representations
Power
To		 Ag E1g* E2g* Au E1u* E2u*
1 0 0 0 0 0 1 E2u
2 1 1 0 0 0 0 Ag⊕E1g
3 0 0 0 0 1 1 E1u⊕E2u
4 1 1 1 0 0 0 Ag⊕E1g⊕E2g
5 0 0 0 2 1 1 2Au⊕E1u⊕E2u
6 1 1 2 0 0 0 Ag⊕E1g⊕2E2g
7 0 0 0 2 2 1 2Au⊕2E1u⊕E2u
8 1 2 2 0 0 0 Ag⊕2E1g⊕2E2g
9 0 0 0 2 2 2 2Au⊕2E1u⊕2E2u
10 3 2 2 0 0 0 3Ag⊕2E1g⊕2E2g
11 0 0 0 2 2 3 2Au⊕2E1u⊕3E2u
12 3 3 2 0 0 0 3Ag⊕3E1g⊕2E2g
13 0 0 0 2 3 3 2Au⊕3E1u⊕3E2u
14 3 3 3 0 0 0 3Ag⊕3E1g⊕3E2g
15 0 0 0 4 3 3 4Au⊕3E1u⊕3E2u
16 3 3 4 0 0 0 3Ag⊕3E1g⊕4E2g
17 0 0 0 4 4 3 4Au⊕4E1u⊕3E2u
18 3 4 4 0 0 0 3Ag⊕4E1g⊕4E2g
19 0 0 0 4 4 4 4Au⊕4E1u⊕4E2u
20 5 4 4 0 0 0 5Ag⊕4E1g⊕4E2g


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