Results for Point Group C15



Symmetric powers of degenerate representation E1
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 1.827 1.338 0.618 -0.209 -1 -1.618 -1.956 -1.956 -1.618 -1 -0.209 0.618 1.338 1.827
2 3 2.338 0.791 -0.618 -0.956 0 1.618 2.827 2.827 1.618 0 -0.956 -0.618 0.791 2.338
3 4 2.445 -0.280 -1.000 0.409 1 -1.000 -3.574 -3.574 -1.000 1 0.409 -1.000 -0.280 2.445
4 5 2.129 -1.165 -0.000 0.871 -1 -0.000 4.165 4.165 0.000 -1 0.871 0.000 -1.165 2.129
5 6 1.445 -1.280 1.000 -0.591 0 1.000 -4.574 -4.574 1.000 0 -0.591 1.000 -1.280 1.445
6 7 0.511 -0.547 0.618 -0.747 1 -1.618 4.783 4.783 -1.618 1 -0.747 0.618 -0.547 0.511
7 8 -0.511 0.547 -0.618 0.747 -1 1.618 -4.783 -4.783 1.618 -1 0.747 -0.618 0.547 -0.511
8 9 -1.445 1.280 -1.000 0.591 0 -1.000 4.574 4.574 -1.000 0 0.591 -1.000 1.280 -1.445
9 10 -2.129 1.165 -0.000 -0.871 1 -0.000 -4.165 -4.165 0.000 1 -0.871 0.000 1.165 -2.129
10 11 -2.445 0.280 1.000 -0.409 -1 1.000 3.574 3.574 1.000 -1 -0.409 1.000 0.280 -2.445
11 12 -2.338 -0.791 0.618 0.956 0 -1.618 -2.827 -2.827 -1.618 0 0.956 0.618 -0.791 -2.338
12 13 -1.827 -1.338 -0.618 0.209 1 1.618 1.956 1.956 1.618 1 0.209 -0.618 -1.338 -1.827
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 1.827 1.338 0.618 -0.209 -1 -1.618 -1.956 -1.956 -1.618 -1 -0.209 0.618 1.338 1.827
17 18 2.338 0.791 -0.618 -0.956 0 1.618 2.827 2.827 1.618 0 -0.956 -0.618 0.791 2.338
18 19 2.445 -0.280 -1.000 0.409 1 -1.000 -3.574 -3.574 -1.000 1 0.409 -1.000 -0.280 2.445
19 20 2.129 -1.165 -0.000 0.871 -1 -0.000 4.165 4.165 0.000 -1 0.871 0.000 -1.165 2.129
20 21 1.445 -1.280 1.000 -0.591 0 1.000 -4.574 -4.574 1.000 0 -0.591 1.000 -1.280 1.445


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


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