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 \(C_1\)

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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

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