Characters of symmetric power
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 |
i |
(S30)17 |
(S30)19 |
(S10)7 |
(S30)23 |
(S6)5 |
(S10)9 |
(S30)29 |
S30 |
S10 |
S6 |
(S30)7 |
(S10)3 |
(S30)11 |
(S30)13 |
| 1 |
0 |
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 |
0 |
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 |
| 2 |
0 |
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 |
0 |
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 |
| 3 |
0 |
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 |
0 |
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 |
| 4 |
0 |
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 |
0 |
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 |
| 5 |
0 |
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 |
0 |
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 |
| 6 |
0 |
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 |
0 |
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 |
Decomposition to irreducible representations
Column for irrep E126212232u highlighted
Power
To |
Ag |
E1g*
|
E2g*
|
E3g*
|
E4g*
|
E5g*
|
E6g*
|
E7g*
|
Au |
E1u*
|
E2u*
|
E3u*
|
E4u*
|
E5u*
|
E6u*
|
E7u*
|
| 1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
| 2 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
| 3 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
| 4 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
| 5 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
| 6 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
Contributions to irrep
E126212232u
pos(X) : Position of irreducible representation (irrep) X in character table of S
30
Subtotal: <Contributions to irrep E
126212232u in subsection>
/ <number of nonzero irrep combinations in subsection> / <number of irrep combinations in subsection>
Total: <Contributions to irrep E
126212232u>
/ <number of nonzero irrep combinations in force field> / <number of irrep combinations in force field>
Contributions to irrep
E126212232u for symmetric power to 2
| Irrep combinations (i,i) with indices: pos(Ag) ≤ i ≤ pos(E7u) |
|---|
| Subtotal: 0 / 0 / 16 |
| Irrep combinations (i,j) with indices: pos(Ag) ≤ i ≤ j ≤ pos(E7u) |
|---|
| Subtotal: 0 / 0 / 120 |
| Total: 0 / 0 / 136 |
Contributions to irrep
E126212232u for symmetric power to 3
| Irrep combinations (i,i,i) with indices: pos(Ag) ≤ i ≤ pos(E7u) |
|---|
| Subtotal: 0 / 0 / 16 |
| Irrep combinations (i,i,j) (i,j,j) with indices: pos(Ag) ≤ i ≤ j ≤ pos(E7u) |
|---|
| Subtotal: 0 / 0 / 240 |
| Irrep combinations (i,j,k) with indices: pos(Ag) ≤ i ≤ j ≤ k ≤ pos(E7u) |
|---|
| Subtotal: 0 / 0 / 560 |
| Total: 0 / 0 / 816 |
Contributions to irrep
E126212232u for symmetric power to 4
| Irrep combinations (i,i,i,i) with indices: pos(Ag) ≤ i ≤ pos(E7u) |
|---|
| Subtotal: 0 / 0 / 16 |
| Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(Ag) ≤ i ≤ j ≤ pos(E7u) |
|---|
| Subtotal: 0 / 0 / 240 |
| Irrep combinations (i,i,j,j) with indices: pos(Ag) ≤ i ≤ j ≤ pos(E7u) |
|---|
| Subtotal: 0 / 0 / 120 |
| Irrep combinations (i,i,j,k) (i,j,j,k) (i,j,k,k) with indices: pos(Ag) ≤ i ≤ j ≤ k ≤ pos(E7u) |
|---|
| Subtotal: 0 / 0 / 1.680 |
| Irrep combinations (i,j,k,l) with indices: pos(Ag) ≤ i ≤ j ≤ k ≤ l ≤ pos(E7u) |
|---|
| Subtotal: 0 / 0 / 1.820 |
| Total: 0 / 0 / 3.876 |
Calculate contributions to
Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement