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: | $C_2^2$ |
| Order: | $4$ |
| Abelian: | $\mathrm{True}$ |
Subgroups and Supergroups
| Maximal Subgroups: | $F_a$, $F_{ab}$ |
| Minimal Supergroups: |
Moment Statistics
| $x$ | $\mathrm{E}[x^{0}]$ | $\mathrm{E}[x^{1}]$ | $\mathrm{E}[x^{2}]$ | $\mathrm{E}[x^{3}]$ | $\mathrm{E}[x^{4}]$ | $\mathrm{E}[x^{5}]$ | $\mathrm{E}[x^{6}]$ | $\mathrm{E}[x^{7}]$ | $\mathrm{E}[x^{8}]$ | $\mathrm{E}[x^{9}]$ | $\mathrm{E}[x^{10}]$ | $\mathrm{E}[x^{11}]$ | $\mathrm{E}[x^{12}]$ |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_1$ | $1$ | $0$ | $2$ | $0$ | $12$ | $0$ | $110$ | $0$ | $1260$ | $0$ | $16002$ | $0$ | $213906$ |
| $a_2$ | $1$ | $2$ | $5$ | $14$ | $49$ | $202$ | $944$ | $4720$ | $24553$ | $130658$ | $705880$ | $3855040$ | $21232468$ |
Event Probabilities
| $\mathrm{P}[a_1=0]=\frac{1}{4}$ |
| $\mathrm{P}[a_2=2]=\frac{3}{4}$ |