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d5d - Tablice symetrii grup punktowych
D5d grupa punktowa
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| nieabelowe, nieredukowalne reprezentacje 8(12) | |
Podgrupy D5d grupy punktowej: Cs, Ci, C2, C5, D5, C5v, S10 |
Tabela charakterów dla grupy punktowej D5d
|
E
| 2C5 |
2(C5)2 |
5C'2 |
i |
2(S10)3 |
2S10 |
5σd |
linear,
rotations |
quadratic |
| A1g |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
|
x2+y2, z2 |
| A2g |
1 |
1 |
1 |
-1 |
1 |
1 |
1 |
-1 |
Rz |
|
| E1g |
2 |
2cos(2π/5) |
2cos(4π/5) |
0 |
2 |
2cos(2π/5) |
2cos(4π/5) |
0 |
(Rx, Ry) |
(xz, yz) |
| E2g |
2 |
2cos(4π/5) |
2cos(2π/5) |
0 |
2 |
2cos(4π/5) |
2cos(2π/5) |
0 |
|
(x2-y2, xy) |
| A1u |
1 |
1 |
1 |
1 |
-1 |
-1 |
-1 |
-1 |
|
|
| A2u |
1 |
1 |
1 |
-1 |
-1 |
-1 |
-1 |
1 |
z |
|
| E1u |
2 |
2cos(2π/5) |
2cos(4π/5) |
0 |
-2 |
-2cos(2π/5) |
-2cos(4π/5) |
0 |
(x, y) |
|
| E2u |
2 |
2cos(4π/5) |
2cos(2π/5) |
0 |
-2 |
-2cos(4π/5) |
-2cos(2π/5) |
0 |
|
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Tabela mnożenia grupy punktowej D5d| | A1g | A2g | E1g | E2g | A1u | A2u | E1u | E2u |
|---|
| A1g | A1g | A2g | E1g | E2g | A1u | A2u | E1u | E2u |
|---|
| A2g | A2g | A1g | E1g | E2g | A2u | A1u | E1u | E2u |
|---|
| E1g | E1g | E1g | A1g+A2g+E2g | E1g+E2g | E1u | E1u | A1u+A2u+E2u | E1u+E2u |
|---|
| E2g | E2g | E2g | E1g+E2g | A1g+A2g+E2g | E2u | E2u | E1u+E2u | A1u+A2u+E2u |
|---|
| A1u | A1u | A2u | E1u | A2u | A1g | A2g | E1g | E2g |
|---|
| A2u | A2u | A1u | E1u | E2u | A2g | A1g | E1g | E2g |
|---|
| E1u | E1u | E1u | A1u+A2u+E2u | E1u+E2u | E1g | E1g | A1g+A2g+E2g | E1g+E2g |
|---|
| E2u | E2u | E2u | E1u+E2u | A1u+A2u+E2u | E2g | E2g | E1g+E2g | A1g+A2g+E2g |
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