Invariants
| Weight: | $1$ |
| Degree: | $4$ |
| $\mathbb{R}$-dimension: | $2$ |
| Components: | $4$ |
| Contained in: | $\mathrm{USp}(4)$ |
| Rational: | $\mathrm{True}$ |
Identity Component
| Name: | $\mathrm{U}(1)\times\mathrm{U}(1)$ |
| Index: | $4$ |
| $\mathbb{R}$-dimension: | $2$ |
| Description: | $\left\{\begin{bmatrix}A&0\\0&B\end{bmatrix}: A,B\in \mathrm{U}(1)\right\}$ |
Component Group
| Name: | $C_4$ |
| Order: | $4$ |
| Abelian: | $\mathrm{True}$ |
Subgroups and Supergroups
| Maximal Subgroups: | $F_{ab}$ |
| Minimal Supergroups: |
Moment Statistics
| $x$ | $\mathrm{E}[x^{0}]$ | $\mathrm{E}[x^{1}]$ | $\mathrm{E}[x^{2}]$ | $\mathrm{E}[x^{3}]$ | $\mathrm{E}[x^{4}]$ | $\mathrm{E}[x^{5}]$ | $\mathrm{E}[x^{6}]$ | $\mathrm{E}[x^{7}]$ | $\mathrm{E}[x^{8}]$ | $\mathrm{E}[x^{9}]$ | $\mathrm{E}[x^{10}]$ | $\mathrm{E}[x^{11}]$ | $\mathrm{E}[x^{12}]$ |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_1$ | $1$ | $0$ | $1$ | $0$ | $9$ | $0$ | $100$ | $0$ | $1225$ | $0$ | $15876$ | $0$ | $213444$ |
| $a_2$ | $1$ | $1$ | $3$ | $10$ | $41$ | $186$ | $912$ | $4656$ | $24425$ | $130402$ | $705368$ | $3854016$ | $21230420$ |
Event Probabilities
| $\mathrm{P}[a_1=0]=\frac{3}{4}$ | |
| $\mathrm{P}[a_2=0]=\frac{2}{4}$ | $\mathrm{P}[a_2=2]=\frac{1}{4}$ |