Characters of symmetric power
Power
To |
E |
S28 |
C14 |
(S28)3 |
C7 |
(S28)5 |
(C14)3 |
S4 |
(C7)2 |
(S28)9 |
(C14)5 |
(S28)11 |
(C7)3 |
(S28)13 |
C2 |
(S28)15 |
(C7)4 |
(S28)17 |
(C14)9 |
(S28)19 |
(C7)5 |
(S4)3 |
(C14)11 |
(S28)23 |
(C7)6 |
(S28)25 |
(C14)13 |
(S28)27 |
| 1 |
0 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
| 2 |
0 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
| 3 |
0 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
| 4 |
0 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
| 5 |
0 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
| 6 |
0 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
Decomposition to irreducible representations
Column for irrep highlighted
Power
To |
A |
B |
E1*
|
E2*
|
E3*
|
E4*
|
E5*
|
E6*
|
E7*
|
E8*
|
E9*
|
E10*
|
E11*
|
E12*
|
E13*
|
| 1 |
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 |
| 3 |
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 |
| 5 |
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 |
Contributions to irrep
pos(X) : Position of irreducible representation (irrep) X in character table of S
28
Subtotal: <Contributions to irrep in subsection>
/ <number of nonzero irrep combinations in subsection> / <number of irrep combinations in subsection>
Total: <Contributions to irrep >
/ <number of nonzero irrep combinations in force field> / <number of irrep combinations in force field>
Contributions to irrep
for symmetric power to 2
| Irrep combinations (i,i) with indices: pos(A) ≤ i ≤ pos(E13) |
|---|
| Subtotal: 0 / 0 / 15 |
| Irrep combinations (i,j) with indices: pos(A) ≤ i ≤ j ≤ pos(E13) |
|---|
| Subtotal: 0 / 0 / 105 |
| Total: 0 / 0 / 120 |
Contributions to irrep
for symmetric power to 3
| Irrep combinations (i,i,i) with indices: pos(A) ≤ i ≤ pos(E13) |
|---|
| Subtotal: 0 / 0 / 15 |
| Irrep combinations (i,i,j) (i,j,j) with indices: pos(A) ≤ i ≤ j ≤ pos(E13) |
|---|
| Subtotal: 0 / 0 / 210 |
| Irrep combinations (i,j,k) with indices: pos(A) ≤ i ≤ j ≤ k ≤ pos(E13) |
|---|
| Subtotal: 0 / 0 / 455 |
| Total: 0 / 0 / 680 |
Contributions to irrep
for symmetric power to 4
| Irrep combinations (i,i,i,i) with indices: pos(A) ≤ i ≤ pos(E13) |
|---|
| Subtotal: 0 / 0 / 15 |
| Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A) ≤ i ≤ j ≤ pos(E13) |
|---|
| Subtotal: 0 / 0 / 210 |
| Irrep combinations (i,i,j,j) with indices: pos(A) ≤ i ≤ j ≤ pos(E13) |
|---|
| Subtotal: 0 / 0 / 105 |
| Irrep combinations (i,i,j,k) (i,j,j,k) (i,j,k,k) with indices: pos(A) ≤ i ≤ j ≤ k ≤ pos(E13) |
|---|
| Subtotal: 0 / 0 / 1.365 |
| Irrep combinations (i,j,k,l) with indices: pos(A) ≤ i ≤ j ≤ k ≤ l ≤ pos(E13) |
|---|
| Subtotal: 0 / 0 / 1.365 |
| Total: 0 / 0 / 3.060 |
Calculate contributions to
Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement