Invariants
| Weight: | $1$ |
| Degree: | $4$ |
| $\mathbb{R}$-dimension: | $1$ |
| Components: | $2$ |
| Contained in: | $\mathrm{USp}(4)$ |
| Rational: | $\mathrm{True}$ |
Identity Component
| Name: | $\mathrm{U}(1)_2$ |
| Index: | $2$ |
| $\mathbb{R}$-dimension: | $1$ |
| Description: | $\left\{\begin{bmatrix}\mathrm{diag}_2(\alpha)&0\\0&\mathrm{diag}_2(\bar\alpha)\end{bmatrix}: \alpha\bar\alpha = 1,\ \alpha\in\mathbb{C}\right\},\ \mathrm{diag}_2(\alpha):=\begin{bmatrix}\alpha&0\\0&\alpha\end{bmatrix}$ |
Component Group
| Name: | $C_2$ |
| Order: | $2$ |
| Abelian: | $\mathrm{True}$ |
Subgroups and Supergroups
| Maximal Subgroups: | $C_1$ |
| Minimal Supergroups: | $C_4$, $C_{4,1}$, $D_2$, $J(C_2)$, $D_{2,1}$, $D_3$, $C_6$ |
Moment Statistics
| $x$ | $\mathrm{E}[x^{0}]$ | $\mathrm{E}[x^{1}]$ | $\mathrm{E}[x^{2}]$ | $\mathrm{E}[x^{3}]$ | $\mathrm{E}[x^{4}]$ | $\mathrm{E}[x^{5}]$ | $\mathrm{E}[x^{6}]$ | $\mathrm{E}[x^{7}]$ | $\mathrm{E}[x^{8}]$ | $\mathrm{E}[x^{9}]$ | $\mathrm{E}[x^{10}]$ | $\mathrm{E}[x^{11}]$ | $\mathrm{E}[x^{12}]$ |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_1$ | $1$ | $0$ | $4$ | $0$ | $48$ | $0$ | $640$ | $0$ | $8960$ | $0$ | $129024$ | $0$ | $1892352$ |
| $a_2$ | $1$ | $2$ | $10$ | $44$ | $230$ | $1212$ | $6628$ | $36696$ | $205766$ | $1162988$ | $6616940$ | $37841256$ | $217331804$ |
Event Probabilities
| $\mathrm{P}[a_1=0]=\frac{1}{2}$ |