D_{5d} |
E |
2C_{5} |
2(C_{5})^{2} |
5C'_{2} |
i |
2(S_{10})^{3} |
2S_{10} |
5_{d} |
linear functions, rotations |
quadratic functions |
cubic functions |
A_{1g} |
+1 |
+1 |
+1 |
+1 |
+1 |
+1 |
+1 |
+1 |
- |
x^{2}+y^{2}, z^{2} |
- |
A_{2g} |
+1 |
+1 |
+1 |
-1 |
+1 |
+1 |
+1 |
-1 |
R_{z} |
- |
- |
E_{1g} |
+2 |
+2cos(2/5) |
+2cos(4/5) |
0 |
+2 |
+2cos(2/5) |
+2cos(4/5) |
0 |
(R_{x}, R_{y}) |
(xz, yz) |
- |
E_{2g} |
+2 |
+2cos(4/5) |
+2cos(2/5) |
0 |
+2 |
+2cos(4/5) |
+2cos(2/5) |
0 |
- |
(x^{2}-y^{2}, xy) |
- |
A_{1u} |
+1 |
+1 |
+1 |
+1 |
-1 |
-1 |
-1 |
-1 |
- |
- |
- |
A_{2u} |
+1 |
+1 |
+1 |
-1 |
-1 |
-1 |
-1 |
+1 |
z |
- |
z^{3}, z(x^{2}+y^{2}) |
E_{1u} |
+2 |
+2cos(2/5) |
+2cos(4/5) |
0 |
-2 |
-2cos(2/5) |
-2cos(4/5) |
0 |
(x, y) |
- |
(xz^{2}, yz^{2}) [x(x^{2}+y^{2}), y(x^{2}+y^{2})] |
E_{2u} |
+2 |
+2cos(4/5) |
+2cos(2/5) |
0 |
-2 |
-2cos(4/5) |
-2cos(2/5) |
0 |
- |
- |
[xyz, z(x^{2}-y^{2})] [y(3x^{2}-y^{2}), x(x^{2}-3y^{2})] |