Invariants
| Weight: | $1$ |
| Degree: | $4$ |
| $\mathbb{R}$-dimension: | $4$ |
| Components: | $2$ |
| Contained in: | $\mathrm{USp}(4)$ |
| Rational: | $\mathrm{True}$ |
Identity Component
| Name: | $\mathrm{U}(1)\times\mathrm{SU}(2)$ |
| Index: | $2$ |
| $\mathbb{R}$-dimension: | $4$ |
| Description: | $\left\{\begin{bmatrix}A&0\\0&B\end{bmatrix}: A\in \mathrm{U}(1),\ B\in\mathrm{SU}(2)\right\}$ |
Component Group
| Name: | $C_2$ |
| Order: | $2$ |
| Abelian: | $\mathrm{True}$ |
Subgroups and Supergroups
| Maximal Subgroups: | $G_{1,3}$ |
| Minimal Supergroups: |
Moment Statistics
| $x$ | $\mathrm{E}[x^{0}]$ | $\mathrm{E}[x^{1}]$ | $\mathrm{E}[x^{2}]$ | $\mathrm{E}[x^{3}]$ | $\mathrm{E}[x^{4}]$ | $\mathrm{E}[x^{5}]$ | $\mathrm{E}[x^{6}]$ | $\mathrm{E}[x^{7}]$ | $\mathrm{E}[x^{8}]$ | $\mathrm{E}[x^{9}]$ | $\mathrm{E}[x^{10}]$ | $\mathrm{E}[x^{11}]$ | $\mathrm{E}[x^{12}]$ |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_1$ | $1$ | $0$ | $2$ | $0$ | $11$ | $0$ | $90$ | $0$ | $889$ | $0$ | $9723$ | $0$ | $113322$ |
| $a_2$ | $1$ | $2$ | $5$ | $14$ | $46$ | $172$ | $714$ | $3180$ | $14858$ | $71732$ | $354676$ | $1786072$ | $9127672$ |
Event Probabilities
| $\mathrm{P}[a_2=2]=\frac{1}{2}$ |