Invariants
| Weight: | $1$ |
| Degree: | $4$ |
| $\mathbb{R}$-dimension: | $2$ |
| Components: | $2$ |
| Contained in: | $\mathrm{USp}(4)$ |
| Rational: | $\mathrm{True}$ |
Identity Component
| Name: | $\mathrm{U}(1)\times\mathrm{U}(1)$ |
| Index: | $2$ |
| $\mathbb{R}$-dimension: | $2$ |
| Description: | $\left\{\begin{bmatrix}A&0\\0&B\end{bmatrix}: A,B\in \mathrm{U}(1)\right\}$ |
Component Group
| Name: | $C_2$ |
| Order: | $2$ |
| Abelian: | $\mathrm{True}$ |
Subgroups and Supergroups
| Maximal Subgroups: | $F$ |
| Minimal Supergroups: | $F_{a,b}$ |
Moment Statistics
| $x$ | $\mathrm{E}[x^{0}]$ | $\mathrm{E}[x^{1}]$ | $\mathrm{E}[x^{2}]$ | $\mathrm{E}[x^{3}]$ | $\mathrm{E}[x^{4}]$ | $\mathrm{E}[x^{5}]$ | $\mathrm{E}[x^{6}]$ | $\mathrm{E}[x^{7}]$ | $\mathrm{E}[x^{8}]$ | $\mathrm{E}[x^{9}]$ | $\mathrm{E}[x^{10}]$ | $\mathrm{E}[x^{11}]$ | $\mathrm{E}[x^{12}]$ |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_1$ | $1$ | $0$ | $3$ | $0$ | $21$ | $0$ | $210$ | $0$ | $2485$ | $0$ | $31878$ | $0$ | $427350$ |
| $a_2$ | $1$ | $2$ | $6$ | $20$ | $82$ | $372$ | $1824$ | $9312$ | $48850$ | $260804$ | $1410736$ | $7708032$ | $42460840$ |
Event Probabilities
| $\mathrm{P}[a_2=2]=\frac{1}{2}$ |