| Th | E | 4C3 | 4C3² | 3C2 | i | 4S6 | 4S6⁵ | 3σh | 线性 / 转动linear, rotations | 二次quadratic |
|---|---|---|---|---|---|---|---|---|---|---|
| Ag | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | x²+y²+z² | |
| Eg | 12 | ε−1 | ε*−1 | 12 | 12 | ε−1 | ε*−1 | 12 | (2z²−x²−y², x²−y²) | |
| ↳ 共轭conj. | 1 | ε* | ε | 1 | 1 | ε* | ε | 1 | ||
| Tg | 3 | 0 | 0 | −1 | 3 | 0 | 0 | −1 | (Rx, Ry, Rz) | (xy, xz, yz) |
| Au | 1 | 1 | 1 | 1 | −1 | −1 | −1 | −1 | ||
| Eu | 12 | ε−1 | ε*−1 | 12 | −1−2 | −ε1 | −ε*1 | −1−2 | ||
| ↳ 共轭conj. | 1 | ε* | ε | 1 | −1 | −ε* | −ε | −1 | ||
| Tu | 3 | 0 | 0 | −1 | −3 | 0 | 0 | 1 | (x, y, z) |
\(\varepsilon = \exp(2\pi i/3)\)，\(\varepsilon^{*}\) 为其复共轭。合并后每对复共轭不可约表示相加成一个二维实表示（物理上简并）。; \(\varepsilon^{*}\) is its complex conjugate. Merging adds each conjugate pair into one two-dimensional real representation (physically degenerate).
| 阶 hOrder h | 24 |
|---|---|
| 类数Classes | 8 |
| 所属族Family | 立方 Cubic |
| 代表分子Examples | [Co(NO₂)₆]³⁻, [Fe(py)₆]²⁺（理想化）[Co(NO₂)₆]³⁻, [Fe(py)₆]²⁺ (idealised) |
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.