| C5 | E | C5 | C5² | C5³ | C5⁴ | 线性 / 转动linear, rotations | 二次quadratic |
|---|---|---|---|---|---|---|---|
| A | 1 | 1 | 1 | 1 | 1 | z, Rz | x²+y², z² |
| E1 | 12 | ε2cos72° | ε²2cos144° | ε²*2cos144° | ε*2cos72° | (x, y), (Rx, Ry) | (yz, xz) |
| ↳ 共轭conj. | 1 | ε* | ε²* | ε² | ε | ||
| E2 | 12 | ε²2cos144° | ε*2cos72° | ε2cos72° | ε²*2cos144° | (x²−y², xy) | |
| ↳ 共轭conj. | 1 | ε²* | ε | ε* | ε² |
\(\varepsilon = \exp(2\pi i/5)\)，\(\varepsilon^{*}\) 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 | 5 |
|---|---|
| 类数Classes | 5 |
| 所属族Family | Cn |
| 代表分子Examples | 少见rare |
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.