Characters of symmetric power
Power
To |
E |
C29 |
(C29)2 |
(C29)3 |
(C29)4 |
(C29)5 |
(C29)6 |
(C29)7 |
(C29)8 |
(C29)9 |
(C29)10 |
(C29)11 |
(C29)12 |
(C29)13 |
(C29)14 |
(C29)15 |
(C29)16 |
(C29)17 |
(C29)18 |
(C29)19 |
(C29)20 |
(C29)21 |
(C29)22 |
(C29)23 |
(C29)24 |
(C29)25 |
(C29)26 |
(C29)27 |
(C29)28 |
σh |
S29 |
(S29)31 |
(S29)3 |
(S29)33 |
(S29)5 |
(S29)35 |
(S29)7 |
(S29)37 |
(S29)9 |
(S29)39 |
(S29)11 |
(S29)41 |
(S29)13 |
(S29)43 |
(S29)15 |
(S29)45 |
(S29)17 |
(S29)47 |
(S29)19 |
(S29)49 |
(S29)21 |
(S29)51 |
(S29)23 |
(S29)53 |
(S29)25 |
(S29)55 |
(S29)27 |
(S29)57 |
| 1 |
0 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
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 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
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 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
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 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
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 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
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 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
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 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
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 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
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 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
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 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
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 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
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 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
0.000 |
Decomposition to irreducible representations
Column for irrep E'-1849725120 highlighted
Power
To |
A' |
E'1*
|
E'2*
|
E'3*
|
E'4*
|
E'5*
|
E'6*
|
E'7*
|
E'8*
|
E'9*
|
E'10*
|
E'11*
|
E'12*
|
E'13*
|
E'14*
|
A'' |
E''1*
|
E''2*
|
E''3*
|
E''4*
|
E''5*
|
E''6*
|
E''7*
|
E''8*
|
E''9*
|
E''10*
|
E''11*
|
E''12*
|
E''13*
|
E''14*
|
| 1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
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 |
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 |
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 |
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 |
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 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
Contributions to irrep
E'-1849725120
pos(X) : Position of irreducible representation (irrep) X in character table of C
29h
Subtotal: <Contributions to irrep E'
-1849725120 in subsection>
/ <number of nonzero irrep combinations in subsection> / <number of irrep combinations in subsection>
Total: <Contributions to irrep E'
-1849725120>
/ <number of nonzero irrep combinations in force field> / <number of irrep combinations in force field>
Contributions to irrep
E'-1849725120 for symmetric power to 2
| Irrep combinations (i,i) with indices: pos(A') ≤ i ≤ pos(E''14) |
|---|
| Subtotal: 0 / 0 / 30 |
| Irrep combinations (i,j) with indices: pos(A') ≤ i ≤ j ≤ pos(E''14) |
|---|
| Subtotal: 0 / 0 / 435 |
| Total: 0 / 0 / 465 |
Contributions to irrep
E'-1849725120 for symmetric power to 3
| Irrep combinations (i,i,i) with indices: pos(A') ≤ i ≤ pos(E''14) |
|---|
| Subtotal: 0 / 0 / 30 |
| Irrep combinations (i,i,j) (i,j,j) with indices: pos(A') ≤ i ≤ j ≤ pos(E''14) |
|---|
| Subtotal: 0 / 0 / 870 |
| Irrep combinations (i,j,k) with indices: pos(A') ≤ i ≤ j ≤ k ≤ pos(E''14) |
|---|
| Subtotal: 0 / 0 / 4.060 |
| Total: 0 / 0 / 4.960 |
Contributions to irrep
E'-1849725120 for symmetric power to 4
| Irrep combinations (i,i,i,i) with indices: pos(A') ≤ i ≤ pos(E''14) |
|---|
| Subtotal: 0 / 0 / 30 |
| Irrep combinations (i,i,i,j) (i,j,j,j) with indices: pos(A') ≤ i ≤ j ≤ pos(E''14) |
|---|
| Subtotal: 0 / 0 / 870 |
| Irrep combinations (i,i,j,j) with indices: pos(A') ≤ i ≤ j ≤ pos(E''14) |
|---|
| Subtotal: 0 / 0 / 435 |
| Irrep combinations (i,i,j,k) (i,j,j,k) (i,j,k,k) with indices: pos(A') ≤ i ≤ j ≤ k ≤ pos(E''14) |
|---|
| Subtotal: 0 / 0 / 12.180 |
| Irrep combinations (i,j,k,l) with indices: pos(A') ≤ i ≤ j ≤ k ≤ l ≤ pos(E''14) |
|---|
| Subtotal: 0 / 0 / 27.405 |
| Total: 0 / 0 / 40.920 |
Calculate contributions to
Last update November, 13th 2023 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement