Results for Point Group C15



Symmetric powers of degenerate representation E7
Vibrational overtones


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


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


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