# Properties

 Label 1.4.10.1.1a Name $$\mathrm{USp}(4)$$ Weight 1 Degree 4 Real dimension 10 Components 1 Contained in $$\mathrm{USp}(4)$$ Identity Component $$\mathrm{USp}(4)$$ Component group $$C_1$$

## 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

$x$ $\mathrm{E}[x^{0}]$ $\mathrm{E}[x^{1}]$ $\mathrm{E}[x^{2}]$ $\mathrm{E}[x^{3}]$ $\mathrm{E}[x^{4}]$ $\mathrm{E}[x^{5}]$ $\mathrm{E}[x^{6}]$ $\mathrm{E}[x^{7}]$ $\mathrm{E}[x^{8}]$ $\mathrm{E}[x^{9}]$ $\mathrm{E}[x^{10}]$ $\mathrm{E}[x^{11}]$ $\mathrm{E}[x^{12}]$
$a_1$ $1$ $0$ $1$ $0$ $3$ $0$ $14$ $0$ $84$ $0$ $594$ $0$ $4719$
$a_2$ $1$ $1$ $2$ $4$ $10$ $27$ $82$ $268$ $940$ $3476$ $13448$ $53968$ $223412$