Properties

Label 1.4.2.2.1b
  
Name \(F_{ab}\)
Weight 1
Degree 4
Real dimension 2
Components 2
Contained in \(\mathrm{USp}(4)\)
Identity Component \(\mathrm{U}(1)\times\mathrm{U}(1)\)
Component group \(C_2\)

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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:$F_{a,b}$, $F_{ac}$

Moment Statistics

$x$ $\mathrm{E}[x^{0}]$ $\mathrm{E}[x^{1}]$ $\mathrm{E}[x^{2}]$ $\mathrm{E}[x^{3}]$ $\mathrm{E}[x^{4}]$ $\mathrm{E}[x^{5}]$ $\mathrm{E}[x^{6}]$ $\mathrm{E}[x^{7}]$ $\mathrm{E}[x^{8}]$ $\mathrm{E}[x^{9}]$ $\mathrm{E}[x^{10}]$ $\mathrm{E}[x^{11}]$ $\mathrm{E}[x^{12}]$
$a_1$ $1$ $0$ $2$ $0$ $18$ $0$ $200$ $0$ $2450$ $0$ $31752$ $0$ $426888$
$a_2$ $1$ $2$ $6$ $20$ $82$ $372$ $1824$ $9312$ $48850$ $260804$ $1410736$ $7708032$ $42460840$

Event Probabilities

$\mathrm{P}[a_1=0]=\frac{1}{2}$
$\mathrm{P}[a_2=2]=\frac{1}{2}$