Invariants
| Weight: | $1$ |
| Degree: | $4$ |
| $\mathbb{R}$-dimension: | $1$ |
| Components: | $1$ |
| Contained in: | $\mathrm{USp}(4)$ |
| Rational: | $\mathrm{True}$ |
Identity Component
| Name: | $\mathrm{U}(1)_2$ |
| Index: | $1$ |
| $\mathbb{R}$-dimension: | $1$ |
| Description: | $\left\{\begin{bmatrix}\mathrm{diag}_2(\alpha)&0\\0&\mathrm{diag}_2(\bar\alpha)\end{bmatrix}: \alpha\bar\alpha = 1,\ \alpha\in\mathbb{C}\right\},\ \mathrm{diag}_2(\alpha):=\begin{bmatrix}\alpha&0\\0&\alpha\end{bmatrix}$ |
Subgroups and Supergroups
| Maximal Subgroups: | |
| Minimal Supergroups: | $C_2$, $J(C_1)$, $C_{2,1}$, $C_3$ |
Moment Statistics
| $x$ | $\mathrm{E}[x^{0}]$ | $\mathrm{E}[x^{1}]$ | $\mathrm{E}[x^{2}]$ | $\mathrm{E}[x^{3}]$ | $\mathrm{E}[x^{4}]$ | $\mathrm{E}[x^{5}]$ | $\mathrm{E}[x^{6}]$ | $\mathrm{E}[x^{7}]$ | $\mathrm{E}[x^{8}]$ | $\mathrm{E}[x^{9}]$ | $\mathrm{E}[x^{10}]$ | $\mathrm{E}[x^{11}]$ | $\mathrm{E}[x^{12}]$ |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_1$ | $1$ | $0$ | $8$ | $0$ | $96$ | $0$ | $1280$ | $0$ | $17920$ | $0$ | $258048$ | $0$ | $3784704$ |
| $a_2$ | $1$ | $4$ | $18$ | $88$ | $454$ | $2424$ | $13236$ | $73392$ | $411462$ | $2325976$ | $13233628$ | $75682512$ | $434662684$ |