| D3h | E | 2C3 | 3C2 | σh | 2S3 | 3σv | 线性 / 转动linear, rotations | 二次quadratic |
|---|---|---|---|---|---|---|---|---|
| A′1 | 1 | 1 | 1 | 1 | 1 | 1 | x²+y², z² | |
| A′2 | 1 | 1 | −1 | 1 | 1 | −1 | Rz | |
| E′ | 2 | −1 | 0 | 2 | −1 | 0 | (x, y) | (x²−y², xy) |
| A″1 | 1 | 1 | 1 | −1 | −1 | −1 | ||
| A″2 | 1 | 1 | −1 | −1 | −1 | 1 | z | |
| E″ | 2 | −1 | 0 | −2 | 1 | 0 | (Rx, Ry) | (xz, yz) |
约化可约表示Reduce a representation
输入可约表示在各类上的特征标,按约化公式 \(n_i = \frac{1}{h}\sum_R g_R\,\chi(R)\,\chi_i(R)^{*}\) 求出各不可约表示出现的次数。
Enter the characters of a reducible representation; the reduction formula gives how many times each irreducible representation occurs.