Invariants
| Weight: | $1$ |
| Degree: | $4$ |
| $\mathbb{R}$-dimension: | $10$ |
| Components: | $1$ |
| Contained in: | $\mathrm{USp}(4)$ |
| Rational: | $\mathrm{True}$ |
Identity Component
| Name: | $\mathrm{USp}(4)$ |
| Index: | $1$ |
| $\mathbb{R}$-dimension: | $10$ |
| Description: | $\Bigl\{ A\in \mathrm{GL}_4(\mathbb{C}):A^{-1}=\bar{A^{\mathrm{t}}},\ A^{\mathrm{t}}\Omega A = \Omega\Bigr\},\ \Omega:=\begin{bmatrix}0&-I_2\\I_2&0\end{bmatrix},\ I_2:=\begin{bmatrix}1&0\\0&1\end{bmatrix}$ |
Moment Statistics
| $x$ | $\mathrm{E}[x^{0}]$ | $\mathrm{E}[x^{1}]$ | $\mathrm{E}[x^{2}]$ | $\mathrm{E}[x^{3}]$ | $\mathrm{E}[x^{4}]$ | $\mathrm{E}[x^{5}]$ | $\mathrm{E}[x^{6}]$ | $\mathrm{E}[x^{7}]$ | $\mathrm{E}[x^{8}]$ | $\mathrm{E}[x^{9}]$ | $\mathrm{E}[x^{10}]$ | $\mathrm{E}[x^{11}]$ | $\mathrm{E}[x^{12}]$ |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| $a_1$ | $1$ | $0$ | $1$ | $0$ | $3$ | $0$ | $14$ | $0$ | $84$ | $0$ | $594$ | $0$ | $4719$ |
| $a_2$ | $1$ | $1$ | $2$ | $4$ | $10$ | $27$ | $82$ | $268$ | $940$ | $3476$ | $13448$ | $53968$ | $223412$ |